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Journal articles on the topic 'Discretization errors'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Geurts, Bernard J. "Analysis of errors occurring in large eddy simulation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1899 (2009): 2873–83. http://dx.doi.org/10.1098/rsta.2009.0001.

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We analyse the effect of second- and fourth-order accurate central finite-volume discretizations on the outcome of large eddy simulations of homogeneous, isotropic, decaying turbulence at an initial Taylor–Reynolds number Re λ =100. We determine the implicit filter that is induced by the spatial discretization and show that a higher order discretization also induces a higher order filter, i.e. a low-pass filter that keeps a wider range of flow scales virtually unchanged. The effectiveness of the implicit filtering is correlated with the optimal refinement strategy as observed in an error-lands

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2

Nilsen, Halvor M., K. A. A. Lie, and Jostein R. Natvig. "Accurate Modeling of Faults by Multipoint, Mimetic, and Mixed Methods." SPE Journal 17, no. 02 (2012): 568–79. http://dx.doi.org/10.2118/149690-pa.

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Summary The predominant way of modeling faults in industry-standard flow simulators is to introduce so-called transmissibility multipliers in the underlying two-point discretization. Although this approach provides adequate accuracy in many practical cases, two-point discretizations are only consistent for K-orthogonal grids and may introduce significant discretization errors for grids that severely depart from being K-orthogonal. Such grid-distortion errors can be avoided by lateral or vertical stair-stepping of deviated faults at the expense of errors in the geometrical fault description. In

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Zhang, Peng, Jie Wang, Yihao Yang, Shuai Liu, and Jingtao Huang. "On Full-Order Flux Observer and Its Discretization for Induction Motor Control." Electronics 14, no. 5 (2025): 916. https://doi.org/10.3390/electronics14050916.

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Accurate flux observation is crucial for the high-performance control of induction motors (IMs). Implementing a full-order flux observer algorithm in digital controllers requires discretizing the continuous-domain full-order flux observer. However, the errors introduced by discretization increase with rising rotor speed. In the field-weakening region, inappropriate discretization methods can lead to significant flux estimation errors, severely affecting the performance of model predictive control-based induction motors and potentially causing system instability. To enhance the convergence spee

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Carmon, G., N. Mamman, and M. Feingold. "Discretization errors in particle tracking." Physica A: Statistical Mechanics and its Applications 376 (March 2007): 117–32. http://dx.doi.org/10.1016/j.physa.2006.10.048.

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5

Li, Long-yuan, and Peter Bettess. "Adaptive Finite Element Methods: A Review." Applied Mechanics Reviews 50, no. 10 (1997): 581–91. http://dx.doi.org/10.1115/1.3101670.

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The adaptive finite element method (FEM) was developed in the early 1980s. The basic concept of adaptivity developed in the FEM is that, when a physical problem is analyzed using finite elements, there exist some discretization errors caused owing to the use of the finite element model. These errors are calculated in order to assess the accuracy of the solution obtained. If the errors are large, then the finite element model is refined through reducing the size of elements or increasing the order of interpolation functions. The new model is re-analyzed and the errors in the new model are recal

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Kyei, Yaw. "Effective Source Term Discretizations for Higher Accuracy Finite Volume Discretization of Parabolic Equations." International Journal for Innovation Education and Research 9, no. 8 (2021): 366–92. http://dx.doi.org/10.31686/ijier.vol9.iss8.3305.

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A finite volume method is applied to develop space-time discretizations for parabolic equations based on an equation error method.A space-time expansion of the local equation error based on flux integral formulation of the equation is first designed using a desiredframework of neighboring quadrature points for the solution and local source terms. The quadrature weights are then determined through aminimization process for the error which constitutes all local compact fluxes about each centroid within the computational domain.In utilizing a local source term distribution to account for diffusiv

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Mao, Meiliang, Huajun Zhu, Xiaogang Deng, Yaobing Min, and Huayong Liu. "Effect of Geometric Conservation Law on Improving Spatial Accuracy for Finite Difference Schemes on Two-Dimensional Nonsmooth Grids." Communications in Computational Physics 18, no. 3 (2015): 673–706. http://dx.doi.org/10.4208/cicp.250614.060215a.

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AbstractIt is well known that grid discontinuities have significant impact on the performance of finite difference schemes (FDSs). The geometric conservation law (GCL) is very important for FDSs on reducing numerical oscillations and ensuring free-stream preservation in curvilinear coordinate system. It is not quite clear how GCL works in finite difference method and how GCL errors affect spatial discretization errors especially in nonsmooth grids. In this paper, a method is developed to analyze the impact of grid discontinuities on the GCL errors and spatial discretization errors. A violation

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Kahla, Nabil Ben, Saeed AlQadhi, and Mohd Ahmed. "Radial Point Interpolation-Based Error Recovery Estimates for Finite Element Solutions of Incompressible Elastic Problems." Applied Sciences 13, no. 4 (2023): 2366. http://dx.doi.org/10.3390/app13042366.

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Error estimation and adaptive applications help to control the discretization errors in finite element analysis. The study implements the radial point interpolation (RPI)-based error-recovery approaches in finite element analysis. The displacement/pressure-based mixed approach is used in finite element formulation. The RPI approach considers the radial basis functions (RBF) and polynomials basis functions together to interpolate the finite element solutions, i.e., displacement over influence zones to recover the solution errors. The energy norm is used to represent global and local errors. The

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Kinoshita, Hiroshi, and Hiroshi Nakai. "New Methods for Long-Time Numerical Integration of Planetary Orbits." Symposium - International Astronomical Union 152 (1992): 395–406. http://dx.doi.org/10.1017/s0074180900091439.

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When planetary orbits are numerically integrated for a long time by conventional integrators, the most serious problem is secular errors in the energy and the angular momentum of the planetary system due to discretization (truncation) errors. The secular errors in the energy and the angular momentum mean that the semi-major axes, the eccentricities, and the inclinations of planetary orbits have a secular error which grows linearly with time. Recently symplectic integrators and linear symmetric multistep integrators are found not to produce the secular errors in the energy and the angular momen

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10

Braack, Malte, and Alexandre Ern. "A Posteriori Control of Modeling Errors and Discretization Errors." Multiscale Modeling & Simulation 1, no. 2 (2003): 221–38. http://dx.doi.org/10.1137/s1540345902410482.

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11

Samrowski, Tatiana. "Combined Error Estimates in the Case of Dimension Reduction." Computational Methods in Applied Mathematics 14, no. 1 (2014): 113–34. http://dx.doi.org/10.1515/cmam-2013-0024.

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Abstract. We consider the stationary reaction-diffusion problem in a domain $\Omega \subset \mathbb {R}^3$ having the size along one coordinate direction essentially smaller than along the others. By an energy type argumentation, different simplified models of lower dimension can be deduced and solved numerically. For these models, we derive a guaranteed upper bound of the difference between the exact solution of the original problem and a three-dimensional reconstruction generated by the solution of a dimensionally reduced problem. This estimate of the total error is determined as the sum of

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12

Ying Dong Yan and E. Della Torre. "Discretization errors in numerical micromagnetic models." IEEE Transactions on Magnetics 24, no. 6 (1988): 2368–70. http://dx.doi.org/10.1109/20.92111.

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13

Ladevèze, P., and J. P. Pelle. "Estimation of discretization errors in dynamics." Computers & Structures 81, no. 12 (2003): 1133–48. http://dx.doi.org/10.1016/s0045-7949(03)00033-6.

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14

da Silva, Jéderson, Jucélio Tomás Pereira, and Diego Amadeu F. Torres. "h-adaptive topology optimization considering variations of material properties and energy error density recovery." Engineering Computations 37, no. 9 (2020): 3209–41. http://dx.doi.org/10.1108/ec-10-2019-0464.

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Purpose The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity. Design/methodology/approach The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on bo

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15

Meyer, Fabian, Christian Rohde, and Jan Giesselmann. "A posteriori error analysis for random scalar conservation laws using the stochastic Galerkin method." IMA Journal of Numerical Analysis 40, no. 2 (2019): 1094–121. http://dx.doi.org/10.1093/imanum/drz004.

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Abstract In this article we present an a posteriori error estimator for the spatial–stochastic error of a Galerkin-type discretization of an initial value problem for a random hyperbolic conservation law. For the stochastic discretization we use the stochastic Galerkin method and for the spatial–temporal discretization of the stochastic Galerkin system a Runge–Kutta discontinuous Galerkin method. The estimator is obtained using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework of Dafermos (2016, Hyperbolic Conservation Laws in Continuum Phy

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16

Grooms, I., Y. Lee, and A. J. Majda. "Ensemble Filtering and Low-Resolution Model Error: Covariance Inflation, Stochastic Parameterization, and Model Numerics." Monthly Weather Review 143, no. 10 (2015): 3912–24. http://dx.doi.org/10.1175/mwr-d-15-0032.1.

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Abstract The use of under-resolved models in ensemble data assimilation schemes leads to two kinds of model errors: truncation errors associated with discretization of the large-scale dynamics and errors associated with interactions with subgrid scales. Multiplicative and additive covariance inflation can be used to account for model errors in ensemble Kalman filters, but they do not reduce the model error. Truncation errors can be reduced by increasing the accuracy of the numerical discretization of the large-scale dynamics, and subgrid-scale parameterizations can reduce errors associated wit

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17

Hipp, David, Marlis Hochbruck, and Christian Stohrer. "Unified error analysis for nonconforming space discretizations of wave-type equations." IMA Journal of Numerical Analysis 39, no. 3 (2018): 1206–45. http://dx.doi.org/10.1093/imanum/dry036.

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Abstract This paper provides a unified error analysis for nonconforming space discretizations of linear wave equations in the time domain. We propose a framework that studies wave equations as first-order evolution equations in Hilbert spaces and their space discretizations as differential equations in finite-dimensional Hilbert spaces. A lift operator maps the semidiscrete solution from the approximation space to the continuous space. Our main results are a priori error bounds in terms of interpolation, data and conformity errors of the method. Such error bounds are the key to the systematic

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18

Jacod, J., A. Jakubowski, and J. Mémin. "On asymptotic errors in discretization of processes." Annals of Probability 31, no. 2 (2003): 592–608. http://dx.doi.org/10.1214/aop/1048516529.

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19

Reemtsen, Rembert. "On discretization errors in nonlinear approximation problems." Journal of Approximation Theory 49, no. 3 (1987): 256–73. http://dx.doi.org/10.1016/0021-9045(87)90103-1.

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20

Gopalakrishnan, Jay, Luka Grubišić, and Jeffrey Ovall. "Spectral discretization errors in filtered subspace iteration." Mathematics of Computation 89, no. 321 (2019): 203–28. http://dx.doi.org/10.1090/mcom/3483.

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21

Sablok, R., and K. Aziz. "Upscaling and Discretization Errors in Reservoir Simulation." Petroleum Science and Technology 26, no. 10-11 (2008): 1161–86. http://dx.doi.org/10.1080/10916460701833863.

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22

Kocaleva Vitanova, Mirjana, and Vlado Gičev. "Analysis of discretization errors in microtremor measurements." Geologica Macedonica 39, no. 1 (2025): 47–55. https://doi.org/10.46763/geol2539147kv.

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This study investigates the effects of discretization errors on the analysis of microtremor vibrations measured in a building located in Berovo, using the EQR120 accelerometer. The primary focus is on the impact of discretization on Fourier spectral amplitudes and the accuracy of frequency domain analysis. The results show that with increasing recording time (T), there are more pronounced peaks in the Fourier spectrum, especially for higher frequencies. Despite variations in discrete levels of acceleration, the frequency domain response of the instrument remains nearly constant over a wide ran

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23

Andrun, Martina, Branko Blagojević, and Josip Bašić. "The influence of numerical parameters in the finite-volume method on the Wigley hull resistance." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 233, no. 4 (2018): 1123–32. http://dx.doi.org/10.1177/1475090218812956.

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The equations discretization errors are often overlooked compared to the spatial discretization errors. This article presents the results of the influence of various equations discretization schemes in computational fluid dynamics on the prediction of the ship resistance and wave elevation on the hull. For the analysis, steady flow around a model of the Wigley hull is numerically predicted by employing a finite-volume method solver based on Reynolds-averaged Navier–Stokes equations and the volume-of-fluid method. Six momentum discretization schemes, three multi-fluid discretization schemes and

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24

Pritchet, David, Newell Moser, Kornel Ehmann, Jian Cao, and Jiaxing Huang. "Quantifying Discretization Errors in Electrophoretically-Guided Micro Additive Manufacturing." Micromachines 9, no. 9 (2018): 447. http://dx.doi.org/10.3390/mi9090447.

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This paper presents process models for a new micro additive manufacturing process termed Electrophoretically-guided Micro Additive Manufacturing (EPμAM). In EPμAM, a planar microelectrode array generates the electric potential distributions which cause colloidal particles to agglomerate and deposit in desired regions. The discrete microelectrode array nature and the used pulse width modulation (PWM) technique for microelectrode actuation create unavoidable process errors—space and time discretization errors—that distort particle trajectories. To combat this, we developed finite element method

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25

Hwang, Jai Hyuk, Doo Man Kim, and Kyoung Ho Lim. "Robustness of Natural Controls of Distributed-Parameter Systems." Journal of Vibration and Acoustics 118, no. 1 (1996): 56–63. http://dx.doi.org/10.1115/1.2889635.

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In this paper, the effect of parameter and spatial discretization errors on the closed-loop behavior of distributed-parameter systems is analyzed for natural controls. If the control force designed on the basis of the postulated system with the parameter and discretization errors is applied to control the actual system, the closed-loop performance of the actual system will be degraded depending on the degree of the errors. The extent of deviation of the closed-loop performance from the expected one is derived and evaluated using operator techniques. It has been found that the extent of the dev

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Zamani, Behnam, and Manfred Koch. "Comparison Between Two Hydrodynamic Models in Simulating Physical Processes of a Reservoir with Complex Morphology: Maroon Reservoir." Water 12, no. 3 (2020): 814. http://dx.doi.org/10.3390/w12030814.

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Two 3D hydrodynamic models, AEM3D and MIKE3, are compared in simulating hydrodynamics of the Maroon Reservoir in southwest Iran. The reservoir has a complex bathymetry with steep walls, which makes it a good case for studying the performance of hydrodynamic models. The models were compared together and with measured water temperatures from different locations of the reservoir in a five-month period between December 2011 and April 2012. The results indicated that the AEM3D model, which uses a finite difference scheme with a purely z-level vertical discretization, showed better consistency with

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Huang, J., D. V. Griffiths, Andrei V. Lyamin, Kristian Krabbenhoft, and Scott William Sloan. "Discretization Errors of Random Fields in Finite Element Analysis." Applied Mechanics and Materials 553 (May 2014): 405–9. http://dx.doi.org/10.4028/www.scientific.net/amm.553.405.

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The mechanical properties of natural materials such as rocks and soils vary spatially. This randomness is usually modelled by random field theory so that the material properties can be specified at each point in space. When these point-wise material properties are mapped onto a finite element mesh, discretization errors are inevitable. In this study, the discretization errors are studied and suggestions for element sizes in relation with spatial correlation lengths are given.

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R. Maestre, Ismael, Juan Luis Foncubierta Blázquez, Francisco Javier González Gallero, and J. Daniel Mena Baladés. "Effect of Sky Discretization for Shading Device Calculation on Building Energy Performance Simulations." Energies 13, no. 6 (2020): 1381. http://dx.doi.org/10.3390/en13061381.

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The calculation of sunlit surfaces in a building has always been a relevant aspect in building energy simulation programs. Due to the high computational cost, some programs use algorithms for shading calculation for certain solar positions after discretization of hemispherical sky. The influence of the level of discretization on the estimation of incident direct radiation on building surfaces, as well as on the required computational times, are studied in this work. The direct solar energy on a window for a year, with simulation time steps of five minutes, has been simulated by using an algori

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Grübel, Rudolf, and Renate Hermesmeier. "Computation of Compound Distributions II: Discretization Errors and Richardson Extrapolation." ASTIN Bulletin 30, no. 2 (2000): 309–31. http://dx.doi.org/10.2143/ast.30.2.504638.

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AbstractThe standard methods for the calculation of total claim size distributions and ruin probabilities, Panjer recursion and algorithms based on transforms, both apply to lattice-type distributions only and therefore require an initial discretization step if continuous distribution functions are of interest. We discuss the associated discretization error and show that it can often be reduced substantially by an extrapolation technique.

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Kyei, Yaw. "A Residual-Based Numerical Viscosity Regularization Approach for Higher-order Finite Volume Discretization of Scalar Hyperbolic Conservation Laws." International Journal for Innovation Education and Research 12, no. 3 (2024): 22–53. https://doi.org/10.31686/ijier.vol12.iss3.4229.

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A Space-time finite volume method is utilized to construct a parameterized family of two-step explicit higher-order schemes for scalar hyperbolic conservation laws. Utilizing a local space-time expansion of the flux-integral form of the equation error, generalized quadratures of local grid functions of the solution and the associated local source term are formulated to couple grid points within the domains of dependence and influence of new updates about the centroid of each space-time control volume. Optimal quadrature parameters for the discretization are then determined through a minimizati

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31

Abedian, Rooholah. "High-Order Semi-Discrete Central-Upwind Schemes with Lax–Wendroff-Type Time Discretizations for Hamilton–Jacobi Equations." Computational Methods in Applied Mathematics 18, no. 4 (2018): 559–80. http://dx.doi.org/10.1515/cmam-2017-0031.

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AbstractA new fifth-order, semi-discrete central-upwind scheme with a Lax–Wendroff time discretization procedure for solving Hamilton–Jacobi (HJ) equations is presented. This is an alternative method for time discretization to the popular total variation diminishing (TVD) Runge–Kutta time discretizations. Unlike most of the commonly used high-order upwind schemes, the new scheme is formulated as a Godunov-type method. The new scheme is based on the flux Kurganov, Noelle and Petrova (KNP flux). The spatial discretization is based on a symmetrical weighted essentially non-oscillatory reconstruct

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Sun, Jie, Zhaoying Ding, Xiaoshuang Chen, et al. "CREAD: A Classification-Restoration Framework with Error Adaptive Discretization for Watch Time Prediction in Video Recommender Systems." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (2024): 9027–34. http://dx.doi.org/10.1609/aaai.v38i8.28752.

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The watch time is a significant indicator of user satisfaction in video recommender systems. However, the prediction of watch time as a target variable is often hindered by its highly imbalanced distribution with a scarcity of observations for larger target values and over-populated samples for small values. State-of-the-art watch time prediction models discretize the continuous watch time into a set of buckets in order to consider the distribution of watch time. However, it is highly uninvestigated how these discrete buckets should be created from the continuous watch time distribution, and e

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MacMillan, Gordon J., and Jens Schumacher. "Correction of Discretization Errors Simulated at Supply Wells." Groundwater 53, no. 4 (2014): 651–57. http://dx.doi.org/10.1111/gwat.12254.

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Fregly, Benjamin J., and W. Gregory Sawyer. "Estimation of discretization errors in contact pressure measurements." Journal of Biomechanics 36, no. 4 (2003): 609–13. http://dx.doi.org/10.1016/s0021-9290(02)00436-0.

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Lehrenfeld, Christoph, and Maxim Olshanskii. "An Eulerian finite element method for PDEs in time-dependent domains." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 2 (2019): 585–614. http://dx.doi.org/10.1051/m2an/2018068.

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The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in a triangulated computational domain and can overlap the time-independent background mesh in an arbitrary way. The numerical method is based on finite difference discretizations of time derivatives and a standard geometrically unfitted finite element method with an additional stabilization term in the spatial domain. The performance and analysis of the method

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Hänninen, Niko, Aki Pulkkinen, and Tanja Tarvainen. "Image Reconstruction with Reliability Assessment in Quantitative Photoacoustic Tomography." Journal of Imaging 4, no. 12 (2018): 148. http://dx.doi.org/10.3390/jimaging4120148.

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Quantitative photoacoustic tomography is a novel imaging method which aims to reconstruct optical parameters of an imaged target based on initial pressure distribution, which can be obtained from ultrasound measurements. In this paper, a method for reconstructing the optical parameters in a Bayesian framework is presented. In addition, evaluating the credibility of the estimates is studied. Furthermore, a Bayesian approximation error method is utilized to compensate the modeling errors caused by coarse discretization of the forward model. The reconstruction method and the reliability of the cr

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Zhang, Zhongqi, Yiquan Sun, Dongsheng Yu, Peng Mao, and Li Xu. "Influence of Sampling Point Discretization on the Regional Variability of Soil Organic Carbon in the Red Soil Region, China." Sustainability 10, no. 10 (2018): 3603. http://dx.doi.org/10.3390/su10103603.

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Research on the regional variability of soil organic carbon (SOC) has focused mostly on the influence of the number of soil sampling points and interpolation methods. Little attention has typically been paid to the influence of sampling point discretization. Based on dense soil sampling points in the red soil area of Southern China, we obtained four sample discretization levels by a resampling operation. Then, regional SOC distributions were obtained at four levels by two interpolation methods: ordinary Kriging (OK) and Kriging combined with land use information (LuK). To evaluate the influenc

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Naber, Ady, Daniel Berwanger, and Werner Nahm. "Geodesic Length Measurement in Medical Images: Effect of the Discretization by the Camera Chip and Quantitative Assessment of Error Reduction Methods." Photonics 7, no. 3 (2020): 70. http://dx.doi.org/10.3390/photonics7030070.

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After interventions such as bypass surgeries the vascular function is checked qualitatively and remotely by observing the blood dynamics inside the vessel via Fluorescence Angiography. This state-of-the-art method has to be improved by introducing a quantitatively measured blood flow. Previous approaches show that the measured blood flow cannot be easily calibrated against a gold standard reference. In order to systematically address the possible sources of error, we investigated the error in geodesic length measurement caused by spatial discretization on the camera chip. We used an in-silico

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Grudzien, Colin, Marc Bocquet, and Alberto Carrassi. "On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments." Geoscientific Model Development 13, no. 4 (2020): 1903–24. http://dx.doi.org/10.5194/gmd-13-1903-2020.

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Abstract. Relatively little attention has been given to the impact of discretization error on twin experiments in the stochastic form of the Lorenz-96 equations when the dynamics are fully resolved but random. We study a simple form of the stochastically forced Lorenz-96 equations that is amenable to higher-order time-discretization schemes in order to investigate these effects. We provide numerical benchmarks for the overall discretization error, in the strong and weak sense, for several commonly used integration schemes and compare these methods for biases introduced into ensemble-based stat

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Lazarov, Raytcho D., Stanimire Z. Tomov, and Panayot S. Vassilevski. "Interior Penalty Discontinuous Approximations of Elliptic Problems." Computational Methods in Applied Mathematics 1, no. 4 (2001): 367–82. http://dx.doi.org/10.2478/cmam-2001-0024.

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AbstractThis paper studies an interior penalty discontinuous approximation of elliptic problems on nonmatching grids. Error analysis, interface domain decomposition type preconditioners, as well as numerical results illustrating both discretization errors and condition number estimates of the problem and reduced forms of it are presented.

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Liu, Hailiang, and Hairui Wen. "Error estimates of the third order runge-kutta alternating evolution discontinuous galerkin method for convection-diffusion problems." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 5 (2018): 1709–32. http://dx.doi.org/10.1051/m2an/2018020.

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In this paper, we present the stability analysis and error estimates for the alternating evolution discontinuous Galerkin (AEDG) method with third order explicit Runge-Kutta temporal discretization for linear convection-diffusion equations. The scheme is shown stable under a CFL-like stability condition c0τ ≤ ε ≤ c1h2. Here ε is the method parameter, and h is the maximum spatial grid size. We further obtain the optimal L2 error of order O(τ3 + hk+1). Key tools include two approximation finite element spaces to distinguish overlapping polynomials, coupled global projections, and energy estimate

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ADJERID, SLIMANE, JOSEPH E. FLAHERTY, and IVO BABUŠKA. "A POSTERIORI ERROR ESTIMATION FOR THE FINITE ELEMENT METHOD-OF-LINES SOLUTION OF PARABOLIC PROBLEMS." Mathematical Models and Methods in Applied Sciences 09, no. 02 (1999): 261–86. http://dx.doi.org/10.1142/s0218202599000142.

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Babuška and Yu constructed a posteriori estimates for finite element discretization errors of linear elliptic problems utilizing a dichotomy principal stating that the errors of odd-order approximations arise near element edges as mesh spacing decreases while those of even-order approximations arise in element interiors. We construct similar a posteriori estimates for the spatial errors of finite element method-of-lines solutions of linear parabolic partial differential equations on square-element meshes. Error estimates computed in this manner are proven to be asymptotically correct; thus, th

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Danilov, Alexander A., Alexey A. Liogky, and Fyodor A. Syomin. "Temporally and spatially segregated discretization for a coupled electromechanical myocardium model." Russian Journal of Numerical Analysis and Mathematical Modelling 39, no. 5 (2024): 243–58. http://dx.doi.org/10.1515/rnam-2024-0022.

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Abstract In this paper, we propose a novel temporally and spatially segregated numerical scheme to discretize the coupled electromechanical model of myocardium. We perform several numerical experiments with activation of a myocardial slab with structural inhomogeneity and evaluate the dependence of numerical errors on the size of spatial and temporal discretization steps. In our study, we show that the spatial step for the mechanical equations h m ⩽2.5 mm yields reasonable results with noticeable errors only in the region of myocardial inhomogeneity. We also show that time step τ m ⩽1 ms can b

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Xie, Chao-Fan, Hong Zhang, and Rey-Chue Hwang. "Stability and Convergence Analysis of the Discrete Dynamical System for Simulating a Moving Bed." Axioms 13, no. 9 (2024): 586. http://dx.doi.org/10.3390/axioms13090586.

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The efficiency of controlling the simulated moving bed (SMB) has long been a critical issue in the chemical engineering industry. Most existing research relies on finite element methods, which often result in lower control efficiency and are unable to achieve online control. To enhance control over the SMB process, this paper employs the Crank–Nicolson method to develop a discrete dynamical model. This approach allows for the investigation of system stability and convergence, fundamentally addressing the sources of error. During the discretization of partial differential equations (PDEs), two

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McLay, Laura A., and David E. Goldberg. "Efficient Genetic Algorithms Using Discretization Scheduling." Evolutionary Computation 13, no. 3 (2005): 353–85. http://dx.doi.org/10.1162/1063656054794752.

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In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling, or how to vary the discretization within the genetic algorithm in order to use the least amount of computation time for a solution of a desired quality. The effectiveness of discretization scheduling ca

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Mariūnas, Darius, and Vytautas Giniotis. "ANALYSIS OF MODIFIED DISCRETIZATION METHODS FOR THE MEASUREMENT VOLUME." Aviation 8, no. 2 (2004): 21–24. http://dx.doi.org/10.3846/16487788.2004.9635871.

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The analysis performed in the paper shows that the effectiveness of discretization methods depends on the accuracy of the evaluation of the parameters of local surface errors and on the characteristics of the regression polynomial describing them. It is evident from the expressions derived that the wavelength of the distribution errors depends on the number of members of the regression polynomial. By increasing the number of members of the regression polynomial, the wavelength of errors of the surface form will be not evaluated. On the other hand, reducing the number of polynomial members, the

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Eckermann, Stephen D., John P. McCormack, Jun Ma, Timothy F. Hogan, and Katherine A. Zawdie. "Stratospheric Analysis and Forecast Errors Using Hybrid and Sigma Coordinates." Monthly Weather Review 142, no. 1 (2014): 476–85. http://dx.doi.org/10.1175/mwr-d-13-00203.1.

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Abstract Past investigations have documented large divergent wind anomalies in stratospheric reanalyses over steep terrain, which were attributed to discretization errors produced by the terrain-following (sigma) vertical coordinate in the forecast model. However, forecasting experiments have reported negligible differences in skill between sigma- and hybrid-coordinate models. This leads to the paradoxical conclusion that discretization errors in the forecast model yield significant stratospheric analysis errors, but insignificant stratospheric forecast errors. The authors reexamine this issue

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Germanos, R. A. C., and L. F. De Souza. "ANALYSIS OF DISPERSION ERRORS IN ACOUSTIC WAVE SIMULATIONS." Revista de Engenharia Térmica 5, no. 1 (2006): 62. http://dx.doi.org/10.5380/reterm.v5i1.61663.

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The governing equations of the acoustic problem are the compressible Euler equations. The discretization of these equations has to ensure that the acoustic waves are transported with non-dispersive and non-dissipative characteristics. In the present study numerical simulations of a standing acoustic wave are performed. Four different space discretization schemes are tested, namely, a second order finite-differences, a fourth order finitedifferences, a fourth order finite-differences compact scheme and a sixth order finite-differences compact scheme. The time integration is done with a fourth o

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WANG, DONGDONG, and ZHENTING LIN. "A COMPARATIVE STUDY ON THE DISPERSION PROPERTIES OF HRK AND RK MESHFREE APPROXIMATIONS FOR KIRCHHOFF PLATE PROBLEM." International Journal of Computational Methods 09, no. 01 (2012): 1240015. http://dx.doi.org/10.1142/s0219876212400154.

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Dispersion analysis provides a rational way to examine the dynamic properties of numerical methods through comparing the numerical and continuum frequencies. In this paper a detailed comparative investigation is presented on the dispersion features of the Hermite reproducing kernel (HRK) and the conventional reproducing kernel (RK) meshfree methods for Kirchhoff plate problem with particular reference to the spatial discretizations. In the analysis the nodal variables of the semi-discretized meshfree Kirchhoff plate equations are assumed as harmonic wave functions to extract the numerical freq

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Ghidaoui, Mohamed S., Bryan W. Karney, and Duncan A. McInnis. "Energy Estimates for Discretization Errors in Water Hammer Problems." Journal of Hydraulic Engineering 124, no. 4 (1998): 384–93. http://dx.doi.org/10.1061/(asce)0733-9429(1998)124:4(384).

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