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Journal articles on the topic 'Conforming FEM'

Author: Grafiati

Published: 6 September 2023

Last updated: 31 July 2025

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1

Rammerstorfer, Franz, and Martin Schanz. "FEM-BEM coupling with non-conforming interfaces." PAMM 11, no. 1 (2011): 487–88. http://dx.doi.org/10.1002/pamm.201110235.

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2

Wilson, Peter, Tobias Teschemacher, Philipp Bucher, and Roland Wüchner. "Non-conforming FEM-FEM coupling approaches and their application to dynamic structural analysis." Engineering Structures 241 (August 2021): 112342. http://dx.doi.org/10.1016/j.engstruct.2021.112342.

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3

Selzer, Philipp, and Olaf A. Cirpka. "Postprocessing of standard finite element velocity fields for accurate particle tracking applied to groundwater flow." Computational Geosciences 24, no. 4 (2020): 1605–24. http://dx.doi.org/10.1007/s10596-020-09969-y.

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Abstract Particle tracking is a computationally advantageous and fast scheme to determine travel times and trajectories in subsurface hydrology. Accurate particle tracking requires element-wise mass-conservative, conforming velocity fields. This condition is not fulfilled by the standard linear Galerkin finite element method (FEM). We present a projection, which maps a non-conforming, element-wise given velocity field, computed on triangles and tetrahedra, onto a conforming velocity field in lowest-order Raviart-Thomas-Nédélec ($\mathcal {RTN}_{0}$ R T N 0 ) space, which meets the requirements

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4

Margenov, Svetozar, and Nikola Kosturski. "MIC(0) preconditioning of 3D FEM problems on unstructured grids: Conforming and non-conforming elements." Journal of Computational and Applied Mathematics 226, no. 2 (2009): 288–97. http://dx.doi.org/10.1016/j.cam.2008.08.033.

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5

Georgiev, I., J. Kraus, and S. Margenov. "Multilevel preconditioning of rotated bilinear non-conforming FEM problems." Computers & Mathematics with Applications 55, no. 10 (2008): 2280–94. http://dx.doi.org/10.1016/j.camwa.2007.11.008.

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6

Rüberg, Thomas, Martin Schanz, and Gernot Beer. "Non-conforming FEM-BEM coupling for wave propagation phenomena." PAMM 8, no. 1 (2008): 10333–34. http://dx.doi.org/10.1002/pamm.200810333.

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7

Schedensack, Mira. "A New Generalization of the P1 Non-Conforming FEM to Higher Polynomial Degrees." Computational Methods in Applied Mathematics 17, no. 1 (2017): 161–85. http://dx.doi.org/10.1515/cmam-2016-0031.

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AbstractThis paper generalizes the non-conforming FEM of Crouzeix and Raviart and its fundamental projection property by a novel mixed formulation for the Poisson problem based on the Helmholtz decomposition. The new formulation allows for ansatz spaces of arbitrary polynomial degree and its discretization coincides with the mentioned non-conforming FEM for the lowest polynomial degree. The discretization directly approximates the gradient of the solution instead of the solution itself. Besides the a priori and medius analysis, this paper proves optimal convergence rates for an adaptive algori

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8

Margenov, S., and P. Minev. "On a preconditioning of non-conforming mixed FEM elliptic problems." Mathematics and Computers in Simulation 76, no. 1-3 (2007): 149–54. http://dx.doi.org/10.1016/j.matcom.2007.01.021.

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9

Kolev, Tzanio V., and Svetozar D. Margenov. "Two-level preconditioning of pure displacement non-conforming FEM systems." Numerical Linear Algebra with Applications 6, no. 7 (1999): 533–55. http://dx.doi.org/10.1002/(sici)1099-1506(199910/11)6:7<533::aid-nla175>3.0.co;2-7.

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10

XU, X., G. R. LIU, Y. T. GU, and G. Y. ZHANG. "A CONFORMING POINT INTERPOLATION METHOD (CPIM) BY SHAPE FUNCTION RECONSTRUCTION FOR ELASTICITY PROBLEMS." International Journal of Computational Methods 07, no. 03 (2010): 369–95. http://dx.doi.org/10.1142/s0219876210002295.

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A conforming point interpolation method (CPIM) is proposed based on the Galerkin formulation for 2D mechanics problems using triangular background cells. A technique for reconstructing the PIM shape functions is proposed to create a continuous displacement field over the whole problem domain, which guarantees the CPIM passing the standard patch test. We prove theoretically the existence and uniqueness of the CPIM solution, and conduct detailed analyses on the convergence rate; computational efficiency and band width of the stiffness matrix of CPIM. The CPIM does not introduce any additional de

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11

Wahran Shaker and Mohammad Sabawi. "A Posteriori Error Analysis of the FEM Solution for Generic Linear Second-Order ODEs." Academic Science Journal 2, no. 4 (2024): 198–206. http://dx.doi.org/10.24237/asj.02.04.817b.

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In this paper, a posteriori error analysis has been examined and investigated for thecontinuous (conforming) Galerkin finite element method used for solving a generalscalar linear second-order ordinary BVPs.

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12

Besuievsky, G., E. García-Nevado, G. Patow, and B. Beckers. "Procedural modeling buildings for finite element method simulation." Journal of Physics: Conference Series 2042, no. 1 (2021): 012074. http://dx.doi.org/10.1088/1742-6596/2042/1/012074.

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Abstract Finite element methods for heat simulation at urban scale require mesh-volume models, where the meshing process requires a special attention in order to satisfy FEM requirements. In this paper we propose a procedural volume modeling approach for automatic creation of mesh-volume buildings, which are suitable for FEM simulations at urban scale. We develop a basic rule-set library and a building generation procedure that guarantee conforming meshes. In this way, urban models can be easily built for energy analysis. Our test-case shows a street created with building prototypes that fulfi

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13

Mantell, S. C., H. Chanda, J. E. Bechtold, and R. F. Kyle. "A Parametric Study of Acetabular Cup Design Variables Using Finite Element Analysis and Statistical Design of Experiments." Journal of Biomechanical Engineering 120, no. 5 (1998): 667–75. http://dx.doi.org/10.1115/1.2834760.

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To isolate the primary variables influencing acetabular cup and interface stresses, we performed an evaluation of cup loading and cup support variables, using a Statistical Design of Experiments (SDOE) approach. We developed three-dimensional finite element (FEM) models of the pelvis and adjacent bone. Cup support variables included fixation mechanism (cemented or noncemented), amount of bone support, and presence of metal backing. Cup loading variables included head size and cup thickness, cup/head friction, and conformity between the cup and head. Interaction between and among variables was

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14

Gudi, Thirupathi, and Papri Majumder. "Conforming and discontinuous Galerkin FEM in space for solving parabolic obstacle problem." Computers & Mathematics with Applications 78, no. 12 (2019): 3896–915. http://dx.doi.org/10.1016/j.camwa.2019.06.022.

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15

Nadal, E., J. J. Ródenas, J. Albelda, M. Tur, J. E. Tarancón, and F. J. Fuenmayor. "Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/953786.

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This work presents an analysis methodology based on the use of the Finite Element Method (FEM) nowadays considered one of the main numerical tools for solving Boundary Value Problems (BVPs). The proposed methodology, so-called cg-FEM (Cartesian grid FEM), has been implemented for fast and accurate numerical analysis of 2D linear elasticity problems. The traditional FEM uses geometry-conforming meshes; however, in cg-FEM the analysis mesh is not conformal to the geometry. This allows for defining very efficient mesh generation techniques and using a robust integration procedure, to accurately i

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16

Guillén-Oviedo, Helen, Jeremías Ramírez-Jiménez, Esteban Segura-Ugalde, and Filánder Sequeira-Chavarría. "Description and implementation of an algebraic multigrid preconditioner for H1-conforming finite element schemes." Uniciencia 34, no. 2 (2020): 55–81. http://dx.doi.org/10.15359/ru.34-2.4.

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This paper presents detailed aspects regarding the implementation of the Finite Element Method (FEM) to solve a Poisson’s equation with homogeneous boundary conditions. The aim of this paper is to clarify details of this implementation, such as the construction of algorithms, implementation of numerical experiments, and their results. For such purpose, the continuous problem is described, and a classical FEM approach is used to solve it. In addition, a multilevel technique is implemented for an efficient resolution of the corresponding linear system, describing and including some diagrams to e

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17

Guillén-Oviedo, H., J. Ramírez-Jiménez, E. Segura-Ugalde, and F. Sequeira-Chavarría. "Description and implementation of an algebraic multigrid preconditioner for H1-conforming finite element schemes." Uniciencia 34, no. 2 (2020): 55–81. https://doi.org/10.15359/ru.34-2.4.

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This paper presents detailed aspects regarding the implementation of the Finite Element Method (FEM) to solve a Poisson’s equation with homogeneous boundary conditions. The aim of this paper is to clarify details of this implementation, such as the construction of algorithms, implementation of numerical experiments, and their results. For such purpose, the continuous problem is described, and a classical FEM approach is used to solve it. In addition, a multilevel technique is implemented for an efficient resolution of the corresponding linear system, describing and including some diagram

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18

Zhang, Y. F., J. H. Yue, M. Li, and R. P. Niu. "Contact Analysis of Functionally Graded Materials Using Smoothed Finite Element Methods." International Journal of Computational Methods 17, no. 05 (2019): 1940012. http://dx.doi.org/10.1142/s0219876219400127.

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In the paper, the smoothed finite element method (S-FEM) based on linear triangular elements is used to solve 2D solid contact problems for functionally graded materials. Both conforming and nonconforming contacts algorithms are developed using modified Coulomb friction contact models including tangential strength and normal adhesion. Based on the smoothed Galerkin weak form, the system stiffness matrices are created using the formulation procedures of node-based S-FEM (NS-FEM) and edge-based S-FEM (ES-FEM), and the contact interface equations are discretized by contact point-pairs. Then these

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19

Wang, Jianye, and Rui Ma. "Unified a Priori Error Estimate and a Posteriori Error Estimate of CIP-FEM for Elliptic Equations." Advances in Applied Mathematics and Mechanics 8, no. 4 (2016): 517–35. http://dx.doi.org/10.4208/aamm.2014.m834.

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AbstractThis paper is devoted to a unified a priori and a posteriori error analysis of CIP-FEM (continuous interior penalty finite element method) for second-order elliptic problems. Compared with the classic a priori error analysis in literature, our technique can easily apply for any type regularity assumption on the exact solution, especially for the case of lowerH1+sweak regularity under consideration, where 0 ≤s≤ 1/2. Because of the penalty term used in the CIP-FEM, Galerkin orthogonality is lost and Céa Lemma for conforming finite element methods can not be applied immediately when 0≤s≤1

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20

Dond, Asha K., and Amiya K. Pani. "A Priori and A Posteriori Estimates of Conforming and Mixed FEM for a Kirchhoff Equation of Elliptic Type." Computational Methods in Applied Mathematics 17, no. 2 (2017): 217–36. http://dx.doi.org/10.1515/cmam-2016-0041.

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AbstractIn this article, a priori and a posteriori estimates of conforming and expanded mixed finite element methods for a Kirchhoff equation of elliptic type are derived. For the expanded mixed finite element method, a variant of Brouwer’s fixed point argument combined with a monotonicity argument yields the well-posedness of the discrete nonlinear system. Further, a use of both Helmholtz decomposition of $L^{2}$-vector valued functions and the discrete Helmholtz decomposition of the Raviart–Thomas finite elements helps in a crucial way to achieve optimal a priori as well as a posteriori erro

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21

ZHANG, G. Y., G. R. LIU, T. T. NGUYEN, et al. "THE UPPER BOUND PROPERTY FOR SOLID MECHANICS OF THE LINEARLY CONFORMING RADIAL POINT INTERPOLATION METHOD (LC-RPIM)." International Journal of Computational Methods 04, no. 03 (2007): 521–41. http://dx.doi.org/10.1142/s0219876207001308.

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It has been proven by the authors that both the upper and lower bounds in energy norm of the exact solution to elasticity problems can now be obtained by using the fully compatible finite element method (FEM) and linearly conforming point interpolation method (LC-PIM). This paper examines the upper bound property of the linearly conforming radial point interpolation method (LC-RPIM), where the Radial Basis Functions (RBFs) are used to construct shape functions and node-based smoothed strains are used to formulate the discrete system equations. It is found that the LC-RPIM also provides the upp

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22

Hu, Jun, and Mira Schedensack. "Two low-order nonconforming finite element methods for the Stokes flow in three dimensions." IMA Journal of Numerical Analysis 39, no. 3 (2018): 1447–70. http://dx.doi.org/10.1093/imanum/dry021.

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Abstract In this paper, we propose two low-order nonconforming finite element methods (FEMs) for the three-dimensional Stokes flow that generalize the nonconforming FEM of Kouhia & Stenberg (1995, A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow. Comput. Methods Appl. Mech. Eng, 124, 195–212). The finite element spaces proposed in this paper consist of two globally continuous components (one piecewise affine and one enriched component) and one component that is continuous at the midpoints of interior faces. We prove that the discrete Korn in

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23

Ma, Zhaoyang, Yunwei Xu, Shu Li, Qingda Yang, Xingming Guo, and Xianyue Su. "A Conforming A-FEM for Modeling Arbitrary Crack Propagation and Branching in Solids." International Journal of Applied Mechanics 13, no. 01 (2021): 2150010. http://dx.doi.org/10.1142/s1758825121500101.

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In this paper, an improved conforming AFEM (C-AFEM) for efficient modeling of arbitrary crack propagation and branching is proposed and validated. An explicit formulation for branching cracks has been derived within the C-AFEM framework. The conjugate gradient method is integrated into the C-AFEM formulation to solve the local problem that consists of all elements traversed by single or multiple cracks. Multiple numerical evidences show that this new approach can substantially improve the modeling efficiency. The solution accuracy and numerical robustness are also significantly improved.

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24

Din-Kow Sun, L. Vardapetyan, and Z. Cendes. "Two-dimensional curl-conforming singular elements for FEM solutions of dielectric waveguiding structures." IEEE Transactions on Microwave Theory and Techniques 53, no. 3 (2005): 984–92. http://dx.doi.org/10.1109/tmtt.2004.842477.

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25

Roos, Hans-Görg, Despo Savvidou, and Christos Xenophontos. "On the Finite Element Approximation of Fourth-Order Singularly Perturbed Eigenvalue Problems." Computational Methods in Applied Mathematics 22, no. 2 (2022): 465–76. http://dx.doi.org/10.1515/cmam-2021-0130.

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Abstract We consider fourth-order singularly perturbed eigenvalue problems in one-dimension and the approximation of their solution by the h version of the Finite Element Method (FEM). In particular, we use a C 1 {C^{1}} -conforming FEM with piecewise polynomials of degree p ≥ 3 {p\geq 3} defined on an exponentially graded mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error in the eigenvalues is measured in absolute value and the error in the eigenvectors is measured in the energy norm. We also illustrate ou

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26

Qu, Xin, Lijun Su, Zhijun Liu, Xingqian Xu, Fangfang Diao, and Wei Li. "Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration." Advances in Materials Science and Engineering 2020 (December 12, 2020): 1–14. http://dx.doi.org/10.1155/2020/6681214.

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As it is very difficult to construct conforming plate elements and the solutions achieved with conforming elements yield inferior accuracy to those achieved with nonconforming elements on many occasions, nonconforming elements, especially Adini’s element (ACM element), are often recommended for practical usage. However, the convergence, good numerical accuracy, and high computing efficiency of ACM element with irregular physical boundaries cannot be achieved using either the finite element method (FEM) or the numerical manifold method (NMM). The mixed-order NMM with background cells for integr

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27

LUBE, GERT, and GERD RAPIN. "RESIDUAL-BASED STABILIZED HIGHER-ORDER FEM FOR A GENERALIZED OSEEN PROBLEM." Mathematical Models and Methods in Applied Sciences 16, no. 07 (2006): 949–66. http://dx.doi.org/10.1142/s0218202506001418.

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In many numerical schemes for standard turbulence models for the nonstationary, incompressible Navier–Stokes equations, the problem is split into linearized auxiliary problems of advection-diffusion-reaction and of Oseen type. Here we present the numerical analysis of a conforming hp-version for stabilized Galerkin methods of SUPG/PSPG-type of the latter problem whereas the analysis of the former problem is reviewed in Ref. 22. We prove a modified inf–sup condition with a constant, which is independent of the spectral order and the viscosity. Moreover, the analysis of the stabilization paramet

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Carstensen, Carsten, and Stefan A. Funken. "Averaging technique for FE – a posteriori error control in elasticity. Part I: Conforming FEM." Computer Methods in Applied Mechanics and Engineering 190, no. 18-19 (2001): 2483–98. http://dx.doi.org/10.1016/s0045-7825(00)00248-6.

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Carstensen, Carsten, and Benedikt Gräßle. "Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains." Computer Methods in Applied Mechanics and Engineering 425 (May 2024): 116931. http://dx.doi.org/10.1016/j.cma.2024.116931.

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30

Lafontaine, D., E. A. Spence, and J. Wunsch. "A sharp relative-error bound for the Helmholtz h-FEM at high frequency." Numerische Mathematik 150, no. 1 (2021): 137–78. http://dx.doi.org/10.1007/s00211-021-01253-0.

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AbstractFor the h-finite-element method (h-FEM) applied to the Helmholtz equation, the question of how quickly the meshwidth h must decrease with the frequency k to maintain accuracy as k increases has been studied since the mid 80’s. Nevertheless, there still do not exist in the literature any k-explicit bounds on the relative error of the FEM solution (the measure of the FEM error most often used in practical applications), apart from in one dimension. The main result of this paper is the sharp result that, for the lowest fixed-order conforming FEM (with polynomial degree, p, equal to one),

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31

LIU, G. R., Y. LI, K. Y. DAI, M. T. LUAN, and W. XUE. "A LINEARLY CONFORMING RADIAL POINT INTERPOLATION METHOD FOR SOLID MECHANICS PROBLEMS." International Journal of Computational Methods 03, no. 04 (2006): 401–28. http://dx.doi.org/10.1142/s0219876206001132.

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A linearly conforming radial point interpolation method (LC-RPIM) is presented for stress analysis of two-dimensional solids. In the LC-RPIM method, each field node is enclosed by a Voronoi polygon, and the displacement field function is approximated using RPIM shape functions of Kronecker delta function property created by simple interpolation using local nodes and radial basis functions augmented with linear polynomials to guarantee linear consistency. The system equations are then derived using the Galerkin weak form and nodal integration techniques, and the essential boundary conditions ar

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32

Marques, Eva S. V., António B. Pereira, and Francisco J. G. Silva. "Quality Assessment of Laser Welding Dual Phase Steels." Metals 12, no. 8 (2022): 1253. http://dx.doi.org/10.3390/met12081253.

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Since non-conforming parts create waste for industry, generating undesirable costs, it is necessary to set up quality plans that not only guarantee product conformity but also cut the root causes of welding defects by developing the concept of quality at origin. Due to their increasing use in automotive industry, dual phase (DP) steels have been the chosen material for this study. A quality plan for welding DP steel components by laser was developed. This plan is divided into three parts: pre-welding, during and post-welding. A quality assessment regarding mechanical properties, such as hardne

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33

Curto-Cárdenas, David, Jose Calaf-Chica, Pedro Miguel Bravo Díez, Mónica Preciado Calzada, and Maria-Jose Garcia-Tarrago. "Cold Expansion Process with Multiple Balls—Numerical Simulation and Comparison with Single Ball and Tapered Mandrels." Materials 13, no. 23 (2020): 5536. http://dx.doi.org/10.3390/ma13235536.

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Cold expansion technology is an extended method used in aeronautics to increase fatigue life of holes and hence extending inspection intervals. During the cold expansion process, a mechanical mandrel is forced to pass along the hole generating compressive residual hoop stresses. The most widely accepted geometry for this mandrel is the tapered one and simpler options like balls have generally been rejected based on the non-conforming residual hoop stresses derived from their use. In this investigation a novelty process using multiple balls with incremental interference, instead of a single one

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Dong, Zhaonan, Emmanuil H. Georgoulis, and Tristan Pryer. "Recovered finite element methods on polygonal and polyhedral meshes." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 4 (2020): 1309–37. http://dx.doi.org/10.1051/m2an/2019047.

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Recovered Finite Element Methods (R-FEM) have been recently introduced in Georgoulis and Pryer [Comput. Methods Appl. Mech. Eng. 332 (2018) 303–324]. for meshes consisting of simplicial and/or box-type elements. Here, utilising the flexibility of the R-FEM framework, we extend their definition to polygonal and polyhedral meshes in two and three spatial dimensions, respectively. An attractive feature of this framework is its ability to produce arbitrary order polynomial conforming discretizations, yet involving only as many degrees of freedom as discontinuous Galerkin methods over general polyg

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Köster, M., and S. Turek. "The Influence of Higher Order FEM Discretisations on Multigrid Convergence." Computational Methods in Applied Mathematics 6, no. 2 (2006): 221–32. http://dx.doi.org/10.2478/cmam-2006-0011.

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AbstractQuadratic and even higher order finite elements are interesting candidates for the numerical solution of partial differential equations (PDEs) due to their improved approximation properties in comparison to linear approaches. The systems of equations that arise from the discretisation of the underlying (elliptic) PDEs are often solved by iterative solvers like preconditioned Krylow-space methods, while multigrid solvers are still rarely used – which might be caused by the high effort that is associated with the realisation of the necessary data structures as well as smoothing and inter

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Carstensen, Carsten, and Sören Bartels. "Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM." Mathematics of Computation 71, no. 239 (2002): 945–69. http://dx.doi.org/10.1090/s0025-5718-02-01402-3.

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Beirão da Veiga, L., F. Brezzi, L. D. Marini, and A. Russo. "Polynomial preserving virtual elements with curved edges." Mathematical Models and Methods in Applied Sciences 30, no. 08 (2020): 1555–90. http://dx.doi.org/10.1142/s0218202520500311.

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In this paper, we tackle the problem of constructing conforming Virtual Element spaces on polygons with curved edges. Unlike previous VEM approaches for curvilinear elements, the present construction ensures that the local VEM spaces contain all the polynomials of a given degree, thus providing the full satisfaction of the patch test. Moreover, unlike standard isoparametric FEM, this approach allows to deal with curved edges at an intermediate scale, between the small scale (treatable by homogenization) and the bigger one (where a finer mesh would make the curve flatter and flatter). The propo

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Blaheta, R., S. Margenov, and M. Neytcheva. "Uniform estimate of the constant in the strengthened CBS inequality for anisotropic non-conforming FEM systems." Numerical Linear Algebra with Applications 11, no. 4 (2004): 309–26. http://dx.doi.org/10.1002/nla.350.

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39

LIU, G. R., G. Y. ZHANG, K. Y. DAI, et al. "A LINEARLY CONFORMING POINT INTERPOLATION METHOD (LC-PIM) FOR 2D SOLID MECHANICS PROBLEMS." International Journal of Computational Methods 02, no. 04 (2005): 645–65. http://dx.doi.org/10.1142/s0219876205000661.

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A linearly conforming point interpolation method (LC-PIM) is developed for 2D solid problems. In this method, shape functions are generated using the polynomial basis functions and a scheme for the selection of local supporting nodes based on background cells is suggested, which can always ensure the moment matrix is invertible as long as there are no coincide nodes. Galerkin weak form is adopted for creating discretized system equations, and a nodal integration scheme with strain smoothing operation is used to perform the numerical integration. The present LC-PIM can guarantee linear exactnes

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Moezzibadi, Mohammad, Isabelle Charpentier, Adrien Wanko, and Robert Mosé. "Sensitivity of groundwater flow with respect to the drain–aquifer leakage coefficient." Journal of Hydroinformatics 20, no. 1 (2017): 177–90. http://dx.doi.org/10.2166/hydro.2017.026.

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Abstract Mitigation measures may be used to prevent soil and water pollution from waste disposal, landfill sites, septic or chemical storage tanks. Among them, drains and impervious barriers may be set up. The efficiency of this technique can be evaluated by means of groundwater modeling tools. The groundwater flow and the leakage drain–aquifer interactions are implemented in a conforming finite element method (FEM) and a mixed hybrid FEM (MHFEM) in a horizontal two-dimensional domain modeling regional aquifer below chemical storage tanks. Considering the influence of uncertainties in the drai

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Vanselow, Reiner. "About Delaunay Triangulations and Discrete Maximum Principles for the Linear Conforming FEM Applied to the Poisson Equation." Applications of Mathematics 46, no. 1 (2001): 13–28. http://dx.doi.org/10.1023/a:1013775420323.

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42

Führer, Thomas, Norbert Heuer, Michael Karkulik, and Rodolfo Rodríguez. "Combining the DPG Method with Finite Elements." Computational Methods in Applied Mathematics 18, no. 4 (2018): 639–52. http://dx.doi.org/10.1515/cmam-2017-0041.

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AbstractWe propose and analyze a discretization scheme that combines the discontinuous Petrov–Galerkin and finite element methods. The underlying model problem is of general diffusion-advection-reaction type on bounded domains, with decomposition into two sub-domains. We propose a heterogeneous variational formulation that is of the ultra-weak (Petrov–Galerkin) form with broken test space in one part, and of Bubnov–Galerkin form in the other. A standard discretization with conforming approximation spaces and appropriate test spaces (optimal test functions for the ultra-weak part and standard t

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Santini, E., D. Vigilante, and F. dell'Isola. "Purely electrical damping of vibrations in arbitrary PEM plates: a mixed non-conforming FEM-Runge-Kutta time evolution analysis." Archive of Applied Mechanics (Ingenieur Archiv) 73, no. 1-2 (2003): 26–48. http://dx.doi.org/10.1007/s00419-002-0251-8.

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Wang, Weilong, Jilian Wu, and Xinlong Feng. "A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 2 (2019): 580–601. http://dx.doi.org/10.1108/hff-06-2018-0265.

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Purpose The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods and to deal with high Rayleigh number for the natural convection problem. Design/methodology/approach The paper introduces a novel characteristic variational multiscale (C-VMS) finite element method which combines advantages of both the characteristic and variational multiscale methods withi

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Song, Yi Jie, Chi On Ho, and Zi Fei Qing. "A Study of New Deployable Structure." Advanced Materials Research 1049-1050 (October 2014): 1083–89. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.1083.

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Deployable structures are new prefabricated frames that can be transformed from a closed stage or compact configuration to a predetermined, stable expanded form. The structure is very convenient for transportation and recycling because it can be stretched out, drawn back and disassembled into pieces easily. This paper describes a new deployable structure composed of scissor composite members, each of which consists of universal scissor components, connected by bolts, and braced by pre-tensioned ropes out-of-plane, conforming a stable system. An aluminum-alloy deployable model was fabricated an

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Radcliffe, A. J. "FEM-BEM coupling for the exterior Stokes problem with non-conforming finite elements and an application to small droplet deformation dynamics." International Journal for Numerical Methods in Fluids 68, no. 4 (2011): 522–36. http://dx.doi.org/10.1002/fld.2518.

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Guo, Hong Wei, Hong Zheng, and Wei Li. "Implement of Ameliorated ACM Element in Numerical Manifold Space for Tackling Kirchhoff Plate Bending Problems." Applied Mechanics and Materials 638-640 (September 2014): 1710–15. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.1710.

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Ab ridging the chasm between the prevalent ly employed continuum methods (e.g. FEM) and discontinuum methods (e.g. DDA) ,the numerical manifold (NNM) ,which utilizes two covers, namely the mathematical cover and physical cover , has evinced various advantages in solving solid mechanic al issues. The forth-order partial elliptic differential equation governing Kirchhoff plate bending makes it arduous to establish the -regular Lagrangian partition of unity ,nevertheless, this study renders a modified conforming ACM manifold element , irrespective of accreting its cover degrees, to resolve the fo

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Jiang, Ying, Minghui Nian, and Qinghui Zhang. "A Stable Generalized Finite Element Method Coupled with Deep Neural Network for Interface Problems with Discontinuities." Axioms 11, no. 8 (2022): 384. http://dx.doi.org/10.3390/axioms11080384.

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The stable generalized finite element method (SGFEM) is an improved version of generalized or extended FEM (GFEM/XFEM), which (i) uses simple and unfitted meshes, (ii) reaches optimal convergence orders, and (iii) is stable and robust in the sense that conditioning is of the same order as that of FEM and does not get bad as interfaces approach boundaries of elements. This paper designs the SGFEM for the discontinuous interface problem (DIP) by coupling a deep neural network (DNN). The main idea is to construct a function using the DNN, which captures the discontinuous interface condition, and

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Xiao, Yingxiong, and Zhenyou Li. "Preconditioned Conjugate Gradient Methods for the Refined FEM Discretizations of Nearly Incompressible Elasticity Problems in Three Dimensions." International Journal of Computational Methods 17, no. 03 (2019): 1850136. http://dx.doi.org/10.1142/s0219876218501360.

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Nearly incompressible problems in three dimensions are the important problems in practical engineering computation. The volume-locking phenomenon will appear when the commonly used finite elements such as linear elements are applied to the solution of these problems. There are many efficient approaches to overcome this locking phenomenon, one of which is the higher-order conforming finite element method. However, we often use the lower-order nonconforming elements as Wilson elements by considering the computational complexity for three-dimensional (3D) problems considered. In general, the conv

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Li, Zhe, Guillaume Oger, and David Le Touzé. "A partitioned framework for coupling LBM and FEM through an implicit IBM allowing non-conforming time-steps: Application to fluid-structure interaction in biomechanics." Journal of Computational Physics 449 (January 2022): 110786. http://dx.doi.org/10.1016/j.jcp.2021.110786.

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