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Journal articles on the topic 'Nonconforming finite element'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Shi, Zhong-Ci. "Nonconforming finite element methods." Journal of Computational and Applied Mathematics 149, no. 1 (2002): 221–25. http://dx.doi.org/10.1016/s0377-0427(02)00531-9.

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2

Li, Youai. "New Error Estimates of Nonconforming Finite Element Methods for the Poisson Problem with Low Regularity Solution." Advances in Applied Mathematics and Mechanics 6, no. 2 (2014): 179–90. http://dx.doi.org/10.4208/aamm.12-m12126.

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AbstractIn this paper, we revisit a priori error analysis of nonconforming finite element methods for the Poisson problem. Based on some techniques developed in the context of the a posteriori error analysis, under two reasonable assumptions on the nonconforming finite element spaces, we prove that, up to some oscillation terms, the consistency error can be bounded by the approximation error. We check these two assumptions for the most used lower order nonconforming finite element methods. Compared with the classical error analysis of the nonconforming finite element method, the a priori analy

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3

Goldstein, Charles I. "Preconditioning Nonconforming Finite Element Methods." SIAM Journal on Numerical Analysis 31, no. 6 (1994): 1623–44. http://dx.doi.org/10.1137/0731084.

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4

Han, Xiaole, Yu Li, and Hehu Xie. "A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods." Numerical Mathematics: Theory, Methods and Applications 8, no. 3 (2015): 383–405. http://dx.doi.org/10.4208/nmtma.2015.m1334.

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AbstractIn this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This correction scheme can increase the overall efficiency of solving eigenvalue problems by the nonconforming finite element method. Furthermore, as same as the direct eigenvalue solving by nonconformi

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5

Lim, Roktaek, and Dongwoo Sheen. "Nonconforming Finite Element Method Applied to the Driven Cavity Problem." Communications in Computational Physics 21, no. 4 (2017): 1012–38. http://dx.doi.org/10.4208/cicp.oa-2016-0039.

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AbstractA cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on P1×P0 on rectangularmeshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those

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6

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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7

Dond, Asha K., Thirupathi Gudi, and Neela Nataraj. "A Nonconforming Finite Element Approximation for Optimal Control of an Obstacle Problem." Computational Methods in Applied Mathematics 16, no. 4 (2016): 653–66. http://dx.doi.org/10.1515/cmam-2016-0024.

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AbstractThe article deals with the analysis of a nonconforming finite element method for the discretization of optimization problems governed by variational inequalities. The state and adjoint variables are discretized using Crouzeix–Raviart nonconforming finite elements, and the control is discretized using a variational discretization approach. Error estimates have been established for the state and control variables. The results of numerical experiments are presented.

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8

Kim, Imbunm, Zhongxuan Luo, Zhaoliang Meng, Hyun Nam, Chunjae Park, and Dongwoo Sheen. "A piecewiseP2-nonconforming quadrilateral finite element." ESAIM: Mathematical Modelling and Numerical Analysis 47, no. 3 (2013): 689–715. http://dx.doi.org/10.1051/m2an/2012044.

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9

Hu, Jun, and Shangyou Zhang. "A Cubic H3-Nonconforming Finite Element." Communications on Applied Mathematics and Computation 1, no. 1 (2019): 81–100. http://dx.doi.org/10.1007/s42967-019-0009-8.

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10

Achchab, Boujemâa, Abdellatif Agouzal, and Khalid Bouihat. "A simple nonconforming quadrilateral finite element." Comptes Rendus Mathematique 352, no. 6 (2014): 529–33. http://dx.doi.org/10.1016/j.crma.2014.03.020.

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11

Lee, Chak Shing, and Dongwoo Sheen. "Nonconforming generalized multiscale finite element methods." Journal of Computational and Applied Mathematics 311 (February 2017): 215–29. http://dx.doi.org/10.1016/j.cam.2016.07.028.

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12

Duan, Huo-Yuan, and Guo-Ping Liang. "Nonconforming elements in least-squares mixed finite element methods." Mathematics of Computation 73, no. 245 (2003): 1–18. http://dx.doi.org/10.1090/s0025-5718-03-01520-5.

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13

Zhang, Shangyou. "Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions." Advances in Applied Mathematics and Mechanics 8, no. 5 (2016): 722–36. http://dx.doi.org/10.4208/aamm.2015.m931.

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AbstractA counterexample is constructed. It confirms that the error of conforming finite element solution is proportional to the coefficient jump, when solving interface elliptic equations. The Scott-Zhang operator is applied to a nonconforming finite element. It is shown that the nonconforming finite element provides the optimal order approximation in interpolation, in L2-projection, and in solving elliptic differential equation, independent of the coefficient jump in the elliptic differential equation. Numerical tests confirm the theoretical finding.

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14

Liu, Huipo, Shuanghu Wang, and Hongbin Han. "Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations." Advances in Applied Mathematics and Mechanics 8, no. 5 (2016): 871–86. http://dx.doi.org/10.4208/aamm.2015.m1104.

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AbstractIn this paper, we consider a least squares nonconforming finite element of low order for solving the transport equations. We give a detailed overview on the stability and the convergence properties of our considered methods in the stability norm. Moreover, we derive residual type a posteriori error estimates for the least squares nonconforming finite element methods underH–1-norm, which can be used as the error indicators to guide the mesh refinement procedure in the adaptive finite element method. The theoretical results are supported by a series of numerical experiments.

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15

Hu, Jun, and ShangYou Zhang. "Nonconforming finite element methods on quadrilateral meshes." Science China Mathematics 56, no. 12 (2013): 2599–614. http://dx.doi.org/10.1007/s11425-013-4741-7.

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16

Chen, Shaochun, Li Yin, and Shipeng Mao. "An anisotropic, superconvergent nonconforming plate finite element." Journal of Computational and Applied Mathematics 220, no. 1-2 (2008): 96–110. http://dx.doi.org/10.1016/j.cam.2007.07.034.

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17

Li, Bo, and Mitchell Luskin. "Nonconforming finite element approximation of crystalline microstructure." Mathematics of Computation 67, no. 223 (1998): 917–47. http://dx.doi.org/10.1090/s0025-5718-98-00941-7.

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18

Braess, D., and R. Verfürth. "Multigrid Methods for Nonconforming Finite Element Methods." SIAM Journal on Numerical Analysis 27, no. 4 (1990): 979–86. http://dx.doi.org/10.1137/0727056.

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19

Liu, Xiaobo. "Interior estimates for nonconforming finite element methods." Numerische Mathematik 74, no. 1 (1996): 49–67. http://dx.doi.org/10.1007/s002110050207.

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20

Capatina-Papaghiuc, Daniela, and Jean-Marie Thomas. "Nonconforming finite element methods without numerical locking." Numerische Mathematik 81, no. 2 (1998): 163–86. http://dx.doi.org/10.1007/s002110050388.

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21

Meng, Zhaoliang, Zhongxuan Luo, and Xinchen Zhou. "A stable nonconforming finite element on hexahedra." International Journal for Numerical Methods in Engineering 109, no. 5 (2016): 611–30. http://dx.doi.org/10.1002/nme.5290.

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22

WALSH, TIMOTHY, GARTH REESE, CLARK DOHRMANN, and JERRY ROUSE. "FINITE ELEMENT METHODS FOR STRUCTURAL ACOUSTICS ON MISMATCHED MESHES." Journal of Computational Acoustics 17, no. 03 (2009): 247–75. http://dx.doi.org/10.1142/s0218396x0900394x.

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In this paper, a new technique is presented for structural acoustic analysis in the case of nonconforming acoustic–solid interface meshes. We first describe a simple method for coupling nonconforming acoustic–acoustic meshes, and then show that a similar approach, together with the coupling operators from conforming analysis, can also be applied to nonconforming structural acoustics. In the case of acoustic–acoustic interfaces, the continuity of acoustic pressure is enforced with a set of linear constraint equations. For structural acoustic interfaces, the same set of linear constraints is use

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23

He, Xiaoxiao. "Superconvergence of a Nonconforming Interface Penalty Finite Element Method for Elliptic Interface Problems." Axioms 14, no. 5 (2025): 364. https://doi.org/10.3390/axioms14050364.

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In our previous works, we developed the superconvergence of a nonconforming finite element method based on unfitted meshes for an elliptic interface problem and elliptic problem, respectively. In this paper, a nonconforming interface penalty finite element method (NIPFEM) based on body-fitted meshes is explored for elliptic interface problems, which allows us to use different meshes in different sub-domains separated by the interface. A nonconforming finite element method based on rectangular meshes is studied and the supercloseness property between the gradient of the numerical solution and t

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24

Zhang, Tong, Shunwei Xu, and Jien Deng. "Stabilized Multiscale Nonconforming Finite Element Method for the Stationary Navier-Stokes Equations." Abstract and Applied Analysis 2012 (2012): 1–27. http://dx.doi.org/10.1155/2012/651808.

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We consider a stabilized multiscale nonconforming finite element method for the two-dimensional stationary incompressible Navier-Stokes problem. This method is based on the enrichment of the standard polynomial space for the velocity component with multiscale function and the nonconforming lowest equal-order finite element pair. Stability and existence uniqueness of the numerical solution are established, optimal-order error estimates are also presented. Finally, some numerical results are presented to validate the performance of the proposed method.

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25

MING, PINGBING, and ZHONG-CI SHI. "NONCONFORMING ROTATED ${\mathcal Q}_1$ ELEMENT FOR REISSNER–MINDLIN PLATE." Mathematical Models and Methods in Applied Sciences 11, no. 08 (2001): 1311–42. http://dx.doi.org/10.1142/s0218202501001343.

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A new locking-free low order nonconforming rectangular finite element for the Reissner–Mindlin plate is presented. It consists of the nonconforming rotated [Formula: see text] element for one of the rotation components and the conforming [Formula: see text] element for the other component together with the conforming [Formula: see text] for the deflection. This element gives optimal error bounds for all variables uniform in the plate thickness t with respect to the energy norm as well as the L2-norm. Moreover, we have derived another nonconforming rectangular element with optimal error bounds

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26

FARHLOUL, M., and M. FORTIN. "A MIXED NONCONFORMING FINITE ELEMENT FOR THE ELASTICITY AND STOKES PROBLEMS." Mathematical Models and Methods in Applied Sciences 09, no. 08 (1999): 1179–99. http://dx.doi.org/10.1142/s0218202599000531.

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A mixed-hybrid formulation of the elasticity problem with a nonconforming symmetric approximation of the stress–tensor is considered. Based on such a formulation, a new finite element of low order with minimal number of degrees of freedom is constructed. Optimal error estimates are derived. Moreover all estimates are valid uniformly with respect to compressibility and apply for the Stokes problem. Finally, an equivalence between this finite element and the piecewise quadratic nonconforming approximation of the elasticity problem is established.

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27

ARNOLD, DOUGLAS N., GERARD AWANOU, and RAGNAR WINTHER. "NONCONFORMING TETRAHEDRAL MIXED FINITE ELEMENTS FOR ELASTICITY." Mathematical Models and Methods in Applied Sciences 24, no. 04 (2014): 783–96. http://dx.doi.org/10.1142/s021820251350067x.

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This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, and which is significantly simpler than any stable conforming mixed finite element method. The method may be viewed as the three-dimensional analogue of a previously developed element in two dimensions. As

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28

Zhang, Xuqing, Yu Zhang, and Yidu Yang. "Guaranteed Lower Bounds for the Elastic Eigenvalues by Using the Nonconforming Crouzeix–Raviart Finite Element." Mathematics 8, no. 8 (2020): 1252. http://dx.doi.org/10.3390/math8081252.

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This paper uses a locking-free nonconforming Crouzeix–Raviart finite element to solve the planar linear elastic eigenvalue problem with homogeneous pure displacement boundary condition. Making full use of the Poincaré inequality, we obtain the guaranteed lower bounds for eigenvalues. Besides, we also use the nonconforming Crouzeix–Raviart finite element to the planar linear elastic eigenvalue problem with the pure traction boundary condition, and obtain the guaranteed lower eigenvalue bounds. Finally, numerical experiments with MATLAB program are reported.

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29

Shi, Zhong-Ci, and Xuejun Xu. "Multigrid for the Wilson Mortar Element Method." Computational Methods in Applied Mathematics 1, no. 1 (2001): 99–112. http://dx.doi.org/10.2478/cmam-2001-0007.

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30

Chen, Fengxin, and Huanzhen Chen. "A Broken P1-Nonconforming Finite Element Method for Incompressible Miscible Displacement Problem in Porous Media." ISRN Applied Mathematics 2013 (December 11, 2013): 1–7. http://dx.doi.org/10.1155/2013/498383.

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An approximate scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by using immersed interface finite element method for the pressure equation which is based on the broken P1-nonconforming piecewise linear polynomials on interface triangular elements and utilizing finite element method for the concentration equation. Error estimates for pressure in broken H1 norm and for concentration in L2 norm are presented.

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31

Efendiev, Yalchin R., Thomas Y. Hou, and Xiao-Hui Wu. "Convergence of a Nonconforming Multiscale Finite Element Method." SIAM Journal on Numerical Analysis 37, no. 3 (2000): 888–910. http://dx.doi.org/10.1137/s0036142997330329.

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32

Gallistl, Dietmar. "Adaptive Nonconforming Finite Element Approximation of Eigenvalue Clusters." Computational Methods in Applied Mathematics 14, no. 4 (2014): 509–35. http://dx.doi.org/10.1515/cmam-2014-0020.

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AbstractThis paper analyses an adaptive nonconforming finite element method for eigenvalue clusters of self-adjoint operators and proves optimal convergence rates (with respect to the concept of nonlinear approximation classes) for the approximation of the invariant subspace spanned by the eigenfunctions of the eigenvalue cluster. Applications include eigenvalues of the Laplacian and of the Stokes system.

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33

Janik, Tadeusz J. "Nonconforming inf-sup conditions for finite element approximations." Numerical Functional Analysis and Optimization 12, no. 3-4 (1991): 361–76. http://dx.doi.org/10.1080/01630569108816434.

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34

Shi, Dongyang, Lele Wang, and Xin Liao. "Nonconforming finite element analysis for Poisson eigenvalue problem." Computers & Mathematics with Applications 70, no. 5 (2015): 835–45. http://dx.doi.org/10.1016/j.camwa.2015.05.029.

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35

Shi, Dongyang, and Buying Zhang. "Nonconforming finite element method for nonlinear parabolic equations." Journal of Systems Science and Complexity 23, no. 2 (2010): 395–402. http://dx.doi.org/10.1007/s11424-010-7120-2.

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36

Risch, Uwe. "Superconvergence of a nonconforming low order finite element." Applied Numerical Mathematics 54, no. 3-4 (2005): 324–38. http://dx.doi.org/10.1016/j.apnum.2004.09.006.

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37

Ortner, C. "Nonconforming finite-element discretization of convex variational problems." IMA Journal of Numerical Analysis 31, no. 3 (2010): 847–64. http://dx.doi.org/10.1093/imanum/drq004.

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38

Yang, Xiaoyuan, and Ruisheng Qi. "Nonconforming finite element method for stochastic Stokes equations." Applied Mathematical Modelling 37, no. 8 (2013): 6110–18. http://dx.doi.org/10.1016/j.apm.2012.12.005.

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39

DongYang, Shi, Feng Weibing, and Li Kaitai. "Nonconforming finite element penalty method for stokes equation." Applied Mathematics-A Journal of Chinese Universities 13, no. 1 (1998): 53–58. http://dx.doi.org/10.1007/s11766-998-0008-4.

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40

Cai, Zhiqiang, and Xiu Ye. "A mixed nonconforming finite element for linear elasticity." Numerical Methods for Partial Differential Equations 21, no. 6 (2005): 1043–51. http://dx.doi.org/10.1002/num.20075.

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41

Lee, Heejeong, and Dongwoo Sheen. "A new quadratic nonconforming finite element on rectangles." Numerical Methods for Partial Differential Equations 22, no. 4 (2006): 954–70. http://dx.doi.org/10.1002/num.20131.

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42

Jang, Gang-Won, Henry Panganiban, and Tae Jin Chung. "P1-nonconforming quadrilateral finite element for topology optimization." International Journal for Numerical Methods in Engineering 84, no. 6 (2010): 685–707. http://dx.doi.org/10.1002/nme.2912.

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43

Meng, Zhaoliang, Zhongxuan Luo, and Dongwoo Sheen. "A new cubic nonconforming finite element on rectangles." Numerical Methods for Partial Differential Equations 31, no. 3 (2014): 691–705. http://dx.doi.org/10.1002/num.21911.

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44

Kaltenbacher, Manfred, and Sebastian Floss. "Nonconforming Finite Elements Based on Nitsche-Type Mortaring for Inhomogeneous Wave Equation." Journal of Theoretical and Computational Acoustics 26, no. 03 (2018): 1850028. http://dx.doi.org/10.1142/s2591728518500287.

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We propose the nonconforming Finite Element (FE) method based on Nitsche-type mortaring for efficiently solving the inhomogeneous wave equation, where due to the change of material properties the wavelength in the subdomains strongly differs. Therewith, we gain the flexibility to choose for each subdomain an optimal grid. The proposed method fulfills the physical conditions along the nonconforming interfaces, namely the continuity of the acoustic pressure and the normal component of the acoustic particle velocity. We apply the nonconforming grid method to the computation of transmission loss (

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45

Jo, Gwanghyun, та J. H. Kim. "A Framework for Nonconforming Mixed Finite Element Method for Elliptic Problems in ℝ3". Journal of Applied Mathematics 2020 (9 квітня 2020): 1–8. http://dx.doi.org/10.1155/2020/2684630.

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In this paper, we suggest a new patch condition for nonconforming mixed finite elements (MFEs) on parallelepiped and provide a framework for the convergence. Also, we introduce a new family of nonconforming MFE space satisfying the new patch condition. The numerical experiments show that the new MFE shows optimal order convergence in Hdiv and L2-norm for various problems with discontinuous coefficient case.

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46

Houédanou, Koffi Wilfrid. "A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot System." Discrete Dynamics in Nature and Society 2022 (March 23, 2022): 1–20. http://dx.doi.org/10.1155/2022/7472965.

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This paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the problem defining the interaction between a free fluid and poroelastic structure. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium is modeled using the Biot poroelasticity system. Equilibrium and kinematic conditions are imposed on the interface. The approach utilizes the same nonconforming Crouzeix–Raviart element discretization on the entire domain. For this discretization, we derive a residual indicator based on the jumps o

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47

Nair, M. Thamban, and Devika Shylaja. "Conforming and nonconforming finite element methods for biharmonic inverse source problem." Inverse Problems 38, no. 2 (2021): 025001. http://dx.doi.org/10.1088/1361-6420/ac3ec5.

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Abstract This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and nonconforming finite element methods (FEMs). The inverse problem is analysed through the forward problem. Error estimate for the forward solution is derived in an abstract set-up that applies to conforming and Morley nonconforming FEMs. Since the inverse problem is ill-posed, Tikhonov regularization is considered to obtain a stable approximate solution. Error

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48

Ji, Xia, Yingxia Xi, and Hehu Xie. "Nonconforming Finite Element Method for the Transmission Eigenvalue Problem." Advances in Applied Mathematics and Mechanics 9, no. 1 (2016): 92–103. http://dx.doi.org/10.4208/aamm.2015.m1295.

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AbstractIn this paper, we analyze a nonconforming finite element method for the computation of transmission eigenvalues and the corresponding eigenfunctions. The error estimates of the eigenvalue and eigenfunction approximation are given, respectively. Finally, some numerical examples are provided to validate the theoretical results.

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49

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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50

YI, SON-YOUNG. "A NEW NONCONFORMING MIXED FINITE ELEMENT METHOD FOR LINEAR ELASTICITY." Mathematical Models and Methods in Applied Sciences 16, no. 07 (2006): 979–99. http://dx.doi.org/10.1142/s0218202506001431.

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We have developed new nonconforming mixed finite element methods for linear elasticity with a pure traction (displacement) boundary condition based on the Hellinger–Reissner variational principle using rectangular elements. Convergence analysis yields an optimal (suboptimal) convergence rate of [Formula: see text] for the L2-error of the stress and [Formula: see text] for the displacement in the pure traction (displacement) boundary problem. However, numerical experiments have yielded optimal-order convergence rates for both stress and displacement in both problems and have shown superconverge

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