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Dissertations / Theses on the topic 'Discretization errors'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Domschke, Pia [Verfasser]. "Adjoint-Based Control of Model and Discretization Errors for Gas Transport in Networked Pipelines / Pia Domschke." München : Verlag Dr. Hut, 2011. http://d-nb.info/1016531443/34.

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2

Kim, Hongman. "Statistical Modeling of Simulation Errors and Their Reduction via Response Surface Techniques." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28390.

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Errors of computational simulations in design of a high-speed civil transport (HSCT) are investigated. First, discretization error from a supersonic panel code, WINGDES, is considered. Second, convergence error from a structural optimization procedure using GENESIS is considered along with the Rosenbrock test problem. A grid converge study is performed to estimate the order of the discretization error in the lift coefficient (CL) of the HSCT calculated from WINGDES. A response surface (RS) model using several mesh sizes is applied to reduce the noise magnification problem associa

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3

Jain, Abhishek. "Modeling of turbulent mixing in combustion LES." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1502969701311144.

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4

Karouma, Abdulrahman. "A Class of Contractivity Preserving Hermite-Birkhoff-Taylor High Order Time Discretization Methods." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32403.

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In this thesis, we study the contractivity preserving, high order, time discretization methods for solving non-stiff ordinary differential equations. We construct a class of one-step, explicit, contractivity preserving, multi-stage, multi-derivative, Hermite-Birkhoff-Taylor methods of order p=5,6, ..., 15, that we denote by CPHBT, with nonnegative coefficients by casting s-stage Runge-Kutta methods of order 4 and 5 with Taylor methods of order p-3 and p-4, respectively. The constructed CPHBT methods are implemented using an efficient variable step algorithm and are compared to other well-kno

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5

Gautham, Tejaswini. "Residual-Based Discretization Error Estimation for Unsteady Flows." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/96400.

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Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is important to have rigorous techniques to estimate the error produced when using CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is extended for the unsteady case. Numerical results

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6

Phillips, Tyrone. "Residual-based Discretization Error Estimation for Computational Fluid Dynamics." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/50647.

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The largest and most difficult numerical approximation error to estimate is discretization error. Residual-based discretization error estimation methods are a category of error estimators that use an estimate of the source of discretization error and information about the specific application to estimate the discretization error using only one grid level. The higher-order terms are truncated from the discretized equations and are the local source of discretization error. The accuracy of the resulting discretization error estimate depends solely on the accuracy of the estimated truncation error

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7

Jalali, Alireza. "Truncation error analysis of unstructured finite volume discretization schemes." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42429.

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Numerical experiments have proved that numerical errors are at least as large as other sources of error in numerical simulation of fluid flows. Approximating the continuous partial differential equations that govern the behavior of a fluid with discrete relations results in truncation error which is the initial source of numerical errors. Reducing numerical error requires the ability to quantify and reduce the truncation error. Although the truncation error can be easily found for structured mesh discretizations, there is no generic methodology for the truncation error analysis of unstructured

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8

Tyson, William Conrad. "Application of r-Adaptation Techniques for Discretization Error Improvement in CFD." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/78061.

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Computational fluid dynamics (CFD) has proven to be an invaluable tool for both engineering design and analysis. As the performance of engineering devices become more reliant upon the accuracy of CFD simulations, it is necessary to not only quantify and but also to reduce the numerical error present in a solution. Discretization error is often the primary source of numerical error. Discretization error is introduced locally into the solution by truncation error. Truncation error represents the higher order terms in an infinite series which are truncated during the discretization of the continu

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9

Hardering, Hanne [Verfasser]. "Intrinsic Discretization Error Bounds for Geodesic Finite Elements / Hanne Hardering." Berlin : Freie Universität Berlin, 2015. http://d-nb.info/1074871022/34.

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10

Niesen, Jitse. "On the global error of discretization methods for ordinary differential equations." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616182.

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11

Phillips, Tyrone. "Extrapolation-based Discretization Error and Uncertainty Estimation in Computational Fluid Dynamics." Thesis, Virginia Tech, 2012. http://hdl.handle.net/10919/31504.

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The solution to partial differential equations generally requires approximations that result in numerical error in the final solution. Of the different types of numerical error in a solution, discretization error is the largest and most difficult error to estimate. In addition, the accuracy of the discretization error estimates relies on the solution (or multiple solutions used in the estimate) being in the asymptotic range. The asymptotic range is used to describe the convergence of a solution, where an asymptotic solution approaches the exact solution at a rate proportional to the change in

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12

Kunert, Gerd, Zoubida Mghazli, and Serge Nicaise. "A posteriori error estimation for a finite volume discretization on anisotropic meshes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601352.

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A singularly perturbed reaction diffusion problem is considered. The small diffusion coefficient generically leads to solutions with boundary layers. The problem is discretized by a vertex-centered finite volume method. The anisotropy of the solution is reflected by using \emph{anisotropic meshes} which can improve the accuracy of the discretization considerably. The main focus is on \emph{a posteriori} error estimation. A residual type error estimator is proposed and rigorously analysed. It is shown to be robust with respect to the small perturbation parameter. The estimator is also robust wi

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13

Wojtas, David Heinrich. "Suppressing Discretization Error in Langevin Simulations of (2+1)-dimensional Field Theories." Thesis, University of Canterbury. Physics and Astronomy, 2006. http://hdl.handle.net/10092/1294.

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Lattice simulations are a popular tool for studying the non-perturbative physics of nonlinear field theories. To perform accurate lattice simulations, a careful account of the discretization error is necessary. Spatial discretization error as a result of lattice spacing dependence in Langevin simulations of anisotropic (2 + 1)-dimensional classical scalar field theories is studied. A transfer integral operator (TIO) method and a one-loop renormalization (1LR) procedure are used to formulate effective potentials. The effective potentials contain counterterms which are intended to suppres

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14

Raju, Anil Roy Christopher J. "Discretization error estimation using the method of nearby problems one-dimensional cases/." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Fall/Thesis/RAJU_ANIL_41.pdf.

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15

Creusé, Emmanuel, Gerd Kunert, and Serge Nicaise. "A posteriori error estimation for the Stokes problem: Anisotropic and isotropic discretizations." Universitätsbibliothek Chemnitz, 2003. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200300057.

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The paper presents a posteriori error estimators for the stationary Stokes problem. We consider anisotropic finite element discretizations (i.e. elements with very large aspect ratio) where conventional, isotropic error estimators fail. Our analysis covers two- and three-dimensional domains, conforming and nonconforming discretizations as well as different elements. This large variety of settings requires different approaches and results in different estimators. Furthermore many examples of finite element pairs that are covered by the analysis are presented. Lower and upper error bounds form

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16

Mavriplis, Cathy. "Nonconforming discretizations and a posteriori error estimators for adaptive spectral element techniques." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/14526.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1989.<br>Includes bibliographical references (leaves 151-157).<br>by Catherine Andria Mavriplis.<br>Ph.D.

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17

Kurzen, Matthew James. "Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems." Thesis, Virginia Tech, 2010. http://hdl.handle.net/10919/31239.

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This work examines the Method of Nearby Problems as a way to generate analytical exact solutions to problems governed by partial differential equations (PDEs). The method involves generating a numerical solution to the original problem of interest, curve fitting the solution, and generating source terms by operating the governing PDEs upon the curve fit. Adding these source terms to the right-hand-side of the governing PDEs defines the nearby problem. In addition to its use for generating exact solutions the MNP can be extended for use as an error estimator. The nearby problem can be solved

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18

Matthews, Charles. "Error in the invariant measure of numerical discretization schemes for canonical sampling of molecular dynamics." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8949.

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Molecular dynamics (MD) computations aim to simulate materials at the atomic level by approximating molecular interactions classically, relying on the Born-Oppenheimer approximation and semi-empirical potential energy functions as an alternative to solving the difficult time-dependent Schrodinger equation. An approximate solution is obtained by discretization in time, with an appropriate algorithm used to advance the state of the system between successive timesteps. Modern MD simulations simulate complex systems with as many as a trillion individual atoms in three spatial dimensions. Many appl

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19

Tyson, William Conrad. "On Numerical Error Estimation for the Finite-Volume Method with an Application to Computational Fluid Dynamics." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/86193.

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Computational fluid dynamics (CFD) simulations can provide tremendous insight into complex physical processes and are often faster and more cost-effective to execute than experiments. However, each CFD result inherently contains numerical errors that can significantly degrade the accuracy of a simulation. Discretization error is typically the largest contributor to the overall numerical error in a given simulation. Discretization error can be very difficult to estimate since the generation, transport, and diffusion of these errors is a highly nonlinear function of the computational grid and di

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20

Sun, Huafei. "Impact of triangle shapes using high-order discretizations and direct mesh adaptation for output error." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/54215.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student submitted PDF version of thesis.<br>Includes bibliographical references (p. 95-101).<br>The impact of triangle shapes, including angle sizes and aspect ratios, on accuracy and stiffness is investigated for simulations of highly anisotropic problems. The results indicate that for high-order discretizations, large a

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21

Maier, Bernhard [Verfasser], and M. [Akademischer Betreuer] Hochbruck. "Error analysis for space and time discretizations of quasilinear wave-type equations / Bernhard Maier ; Betreuer: M. Hochbruck." Karlsruhe : KIT-Bibliothek, 2020. http://d-nb.info/121430155X/34.

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22

Zalewski, Bartlomiej Franciszek. "UNCERTAINTIES IN THE SOLUTIONS TO BOUNDARY ELEMENT METHOD: AN INTERVAL APPROACH." Case Western Reserve University School of Graduate Studies / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=case1212440501.

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23

Carson, Hugh Alexander. "A priori analysis of global and local output error estimates for CG, DG and HDG finite element discretizations." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/105608.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 103-105).<br>In this thesis, a priori convergence estimates are developed for outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Specifically, Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods are analyzed for the Poisson problem. A mixed formulation for DG output error estimation is proposed with improved co

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24

Xue, Weicheng. "CPU/GPU Code Acceleration on Heterogeneous Systems and Code Verification for CFD Applications." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/102073.

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Computational Fluid Dynamics (CFD) applications usually involve intensive computations, which can be accelerated through using open accelerators, especially GPUs due to their common use in the scientific computing community. In addition to code acceleration, it is important to ensure that the code and algorithm are implemented numerically correctly, which is called code verification. This dissertation focuses on accelerating research CFD codes on multi-CPUs/GPUs using MPI and OpenACC, as well as the code verification for turbulence model implementation using the method of manufactured solution

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25

Hipp, David [Verfasser], and M. [Akademischer Betreuer] Hochbruck. "A unified error analysis for spatial discretizations of wave-type equations with applications to dynamic boundary conditions / David Hipp ; Betreuer: M. Hochbruck." Karlsruhe : KIT-Bibliothek, 2017. http://d-nb.info/1136021760/34.

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26

Matthes, Ulrich. "Kontrolle semilinearer elliptischer Randwertprobleme mit variationeller Diskretisierung." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-32879.

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Steuerungsprobleme treten in vielen Anwendungen in Naturwissenschaft und Technik auf. In dieser Arbeit werden Optimalsteuerungsprobleme mit semilinearen elliptischen partiellen Differentialgleichungen als Nebenbedingungen untersucht. Die Kontrolle wird durch Kontrollschranken als Ungleichungsnebenbedingungen eingeschränkt. Dabei ist die Zielfunktion quadratisch in der Kontrolle. Die Lösung des Optimierungsproblems kann dann durch die Projektionsbedingung mit Hilfe des adjungierten Zustandes dargestellt werden. Ein neuer Zugang ist die variationelle Diskretisierung. Bei dieser wird nur der Zu

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27

Veluri, Subrahmanya Pavan Kumar. "Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/28715.

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A detailed code verification study of an unstructured finite volume Computational Fluid Dynamics (CFD) code is performed. The Method of Manufactured Solutions is used to generate exact solutions for the Euler and Navier-Stokes equations to verify the correctness of the code through order of accuracy testing. The verification testing is performed on different mesh types which include triangular and quadrilateral elements in 2D and tetrahedral, prismatic, and hexahedral elements in 3D. The requirements of systematic mesh refinement are discussed, particularly in regards to unstructured meshes. D

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28

Bohinc, Uroš. "Adaptive modeling of plate structures." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2011. http://tel.archives-ouvertes.fr/tel-00675729.

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The primary goal of the thesis is to provide some answers to the questions related to the key steps in the process of adaptive modeling of plates. Since the adaptivity depends on reliable error estimates, a large part of the thesis is related to the derivation of computational procedures for discretization error estimates as well as model error estimates. A practical comparison of some of the established discretization error estimates is made. Special attention is paid to what is called equilibrated residuum method, which has a potential to be used both for discretization error and model error

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29

Wilke, Daniel Nicolas. "Approaches to accommodate remeshing in shape optimization." Thesis, University of Pretoria, 2010. http://hdl.handle.net/2263/24270.

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This study proposes novel optimization methodologies for the optimization of problems that reveal non-physical step discontinuities. More specifically, it is proposed to use gradient-only techniques that do not use any zeroth order information at all for step discontinuous problems. A step discontinuous problem of note is the shape optimization problem in the presence of remeshing strategies, since changes in mesh topologies may - and normally do - introduce non-physical step discontinuities. These discontinuities may in turn manifest themselves as non-physical local minima in which optimizati

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30

Ghavamian, Shahrokh. "Méthode simplifiée pour la simulation du comportement sismique des structures en béton armé : traitement des effets de l'élancement et estimateur d'erreurs." Cachan, Ecole normale supérieure, 1998. http://www.theses.fr/1998DENS0007.

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Le traitement en dynamique non linéaire du fonctionnement des structures en b. A. Est un problème complexe et couteux. L'aborder par des méthodes simplifiées est une solution avantageuse, a la condition de pouvoir conserver une description fine et réaliste des phénomènes majeurs. Analyse dans l'environnement d'une méthode par éléments finis multicouches, il a porte sur deux aspects majeurs : celui du traitement de l'élancement et celui de l'évaluation des erreurs liées a la discrétisation. Le code de calcul eficos initialement conçu avec des éléments poutres de type Navier-Bernoulli composés d

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31

Yang, Shang-Ru, and 楊尚儒. "Correlation Between Discretization Error of Dynamic Loading and Amplitude Distortion for Time Integration." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/ba8pz3.

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碩士<br>國立臺北科技大學<br>土木工程系土木與防災碩士班（碩士在職專班）<br>103<br>In the step-by-step integration procedure, it is important to choose an appropriate time step to obtain a reliable solution. The three basic requirements, stability, accuracy and convergence, must be satisfied. Period distortion is often found in time integration. Hence, a reliable solution can be obtained only if the period distortion is controlled to be relatively small based on accuracy consideration. Period distortion may arise from the difference equations for displacement and velocity, linearization errors and the inaccurate representatio

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32

Peraire, Jaime, and Alexander M. Budge. "Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow." 2002. http://hdl.handle.net/1721.1/4003.

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We introduce a new method for computing a posteriori bounds on engineering outputs from finite element discretizations of the incompressible Stokes equations. The method results from recasting the output problem as a minimization statement without resorting to an error formulation. The minimization statement engenders a duality relationship which we solve approximately by Lagrangian relaxation. We demonstrate the method for a stabilized equal-order approximation of Stokes flow, a problem to which previous output bounding methods do not apply. The conceptual framework for the method is quite ge

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33

Ghaemi, Sina. "Investigation of Effervescent Atomization Using Laser-Based Measurement Techniques." Master's thesis, 2009. http://hdl.handle.net/10048/394.

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Effervescent atomization has been a topic of considerable investigation in the literature due to its important advantages over other atomization mechanisms. This work contributes to the development of both effervescent atomizers and also laser-based techniques for spray investigation In order to develop non-intrusive measurement techniques for spray applications, a procedure is suggested to characterize the shape of droplets using image-based droplet analyzers. Image discretization which is a major source of error in droplet shape measurement is evaluated using a simulation. The accuracy of

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34

Papež, Jan. "Odhady algebraické chyby a zastavovací kritéria v numerickém řešení parciálních diferenciálních rovnic." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-313457.

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Title: Estimation of the algebraic error and stopping criteria in numerical solution of partial differential equations Author: Jan Papež Department: Department of Numerical Mathematics Supervisor of the master thesis: Zdeněk Strakoš Abstract: After introduction of the model problem and its properties we describe the Conjugate Gradient Method (CG). We present the estimates of the energy norm of the error and a heuristic for the adaptive refinement of the estimate. The difference in the local behaviour of the discretization and the algebraic error is illustrated by numerical experiments using th

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35

Matthes, Ulrich. "Kontrolle semilinearer elliptischer Randwertprobleme mit variationeller Diskretisierung." Doctoral thesis, 2009. https://tud.qucosa.de/id/qucosa%3A25276.

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Steuerungsprobleme treten in vielen Anwendungen in Naturwissenschaft und Technik auf. In dieser Arbeit werden Optimalsteuerungsprobleme mit semilinearen elliptischen partiellen Differentialgleichungen als Nebenbedingungen untersucht. Die Kontrolle wird durch Kontrollschranken als Ungleichungsnebenbedingungen eingeschränkt. Dabei ist die Zielfunktion quadratisch in der Kontrolle. Die Lösung des Optimierungsproblems kann dann durch die Projektionsbedingung mit Hilfe des adjungierten Zustandes dargestellt werden. Ein neuer Zugang ist die variationelle Diskretisierung. Bei dieser wird nur der Zu

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36

Wojtas, David H. "Suppressing discretization error in Langevin simulations of (2+1)-dimensional field theories : a thesis submitted in partial fulfilment of the requirements for the degree of Master of Science in Physics in the University of Canterbury /." 2006. http://library.canterbury.ac.nz/etd/adt-NZCU20060728.164114.

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37

Partzsch, Marian. "Neue Verfahren zur Effizienten Simulation Thermischer Systeme mit Translatorischen Strukturvariabilitäten." Doctoral thesis, 2017. https://tud.qucosa.de/id/qucosa%3A31157.

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Aktuelle technologische Herausforderungen, z.B. in der Werkzeugmaschinenentwicklung, erfordern aufgrund der steigenden Genauigkeitsanforderungen an die thermische Simulation eines zu betrachtenden Systems, dass ebenfalls die Auswirkungen relevanter, translatorischer Relativbewegungen zwischen unterschiedlichen Teilen des Systems berücksichtigt werden. Das Vorgehen, diese Bewegung in den Simulationen durch diskrete Verschiebungen zwischen den Lastschritten einer transienten Analyse umzusetzen, führt bei der Verwendung einer infinit kleinen Zeitschrittweite auf die Abbildung einer kontinuierlich

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38

東條, 匡志, and masashi tojo. "Study on the Development of New BWR Core Analysis Scheme Based on the Continuous Energy Monte Carlo Burn-up Calculation Method." Thesis, 2007. http://hdl.handle.net/2237/9665.

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39

Hasnedlová, Jaroslava. "Interakce stlačitelného proudění a struktur." Doctoral thesis, 2012. http://www.nusl.cz/ntk/nusl-309475.

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Title: Fluid-structure interaction of compressible flow Author: RNDr. Jaroslava Hasnedlová Department: Department of Numerical Mathematics, Institute of Applied Mathematics Supervisors: Prof. RNDr. Miloslav Feistauer, DrSc., Dr. h. c., Prof. Dr. Dr. h. c. Rolf Rannacher Supervisors' e-mail addresses: feist@karlin.mff.cuni.cz, rannacher@iwr.uni-heidelberg.de Abstract: The presented work is split into two parts. The first part is devoted to the theory of the discontinuous Galerkin finite element (DGFE) method for the space-time discretization of a nonstationary convection-diffusion initial-bound

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