Anisotropic Nonconforming Crouzeix-Raviart Type FEM for Second Order Elliptic Problems
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摘要: 对满足最大角条件和坐标系条件的二维区域中的各向异性一般三角形网格,研究了二阶椭圆问题的非协调Crouzeix-Raviart型线性三角形有限元逼近,得到了最优的能量模和L2-模误差估计结果.Abstract: The nonconforming Crouzeix-Raviart type linear triangular finite element approximation to second order elliptic problems was studied on anisotropic general triangular meshes in 2D satisfying the maximal angle condition and coordinate system condition. The optimal order error estimates of the broken energy norm and L2 -norm are obtained.
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Key words:
- nonconforming finite element /
- elliptic problems /
- anisotropic meshes
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[1] Ciarlet P G. The Finite Element Method for Elliptic Problems[M]. Amsterdam: North-Holland, 1978. [2] Apel T, Dobrowolski M. Anisotropic interpolation with applications to the finite element method[J]. Computing, 1992, 47(2/3): 277-293. [3] Apel T. Anisotropic Finite Elements: Local Estimates and Applications[M]. Stuttgart, Leipzig: B G Teubner, 1999. [4] Chen S C, Shi D Y, Zhao Y C. Anisotropic interpolations and quasi-Wilson element for narrow quadrilateral meshes[J]. IMA Journal of Numerical Analysis, 2004, 24(1): 77-95. [5] Chen S C, Zhao Y C, Shi D Y. Anisotropic interpolations with application to nonconforming elements[J]. Applied Numerical Mathematics, 2004, 49: 135-152. [6] 石东洋, 梁慧. 各向异性网格下Wilson元的超收敛分析[J]. 应用数学和力学, 2007, 28(1): 107-113.(SHI Dong-yang, LIANG Hui. Superconvergence analysis of Wilson element on anisotropic meshes[J].Applied Mathematics and Mechanics(English Edition), 2007, 28(1): 119-125.) [7] Chen S C, Shi D Y. Accuracy analysis for quasi-Wilson element[J]. Acta Mathematica Scientia B, 2000, 20(1): 44-48. [8] Shi D Y, Chen S C, Hagiwara I. Convergence analysis for a nonconforming membrane element on anisotropic meshes[J]. Journal of Computational Mathematics, 2005, 23(4): 373-382. [9] Shi D Y, Liang H, Wang C X. Superconvergence analysis of a nonconforming triangular element on anisotropic meshes[J]. Journal of Systems Science and Complexity, 2007, 20(4): 536-544. [10] Apel T, Nicaise S, Schberl J. Crouzeix-Raviart type finite elements on anisotropic meshes[J]. Numerische Mathematik, 2001, 89(2): 193-223. [11] Lin Q, Lutz T, Zhou A H. Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation[J]. IMA Journal of Numerical Analysis, 2005, 25(1): 160-181. [12] Shi D Y, Mao S P, Chen S C. Anisotropic nonconforming finite element with some superconvergence results[J]. Journal of Computational Mathematics, 2005, 23(3): 261-274. [13] Shi D Y, Pei L F. Low order Crouzeix-Raviart type nonconforming finite element methods for approximating Maxwell’s equations[J]. International Journal of Numerical Analysis and Modeling, 2008, 5(3): 373-385. [14] Shi D Y, Mao S P, Chen S C. A locking-free anisotropic nonconforming rectangular finite element for planar linear elasticity problems[J]. Acta Mathematica Scientia, B, 2007, 27(1): 193-202. [15] Shi D Y, Wang H H. An anisotropic nonconforming finite element method for approximating a class of nonlinear Sobolev equations[J]. Journal of Computational Mathematics, 2009, 27(2/3):299-314. [16] Shi D Y, Ren J C. Nonconforming mixed finite element approximation to the stationary Navier-Stokes equations on anisotropic meshes[J]. Nonlinear Analysis: Theory, Methods and Applications, 2009, 71(9):3842-3852. [17] Shi D Y, Guan H B. A class of Crouzeix-Raviart type nonconforming finite element methods for parabolic variational inequality problem with moving grid on anisotropic meshes[J].Hokkaido Mathematical Journal, 2007, 36(4): 687-709. [18] Shi D Y, Ren J C, Hao X B. A new second order nonconforming mixed finite element scheme for the stationary Stokes and Navier-Stokes equations[J]. Applied Mathematics and Computation, 2009, 207(2): 462-477. [19] Shi D Y, Liang H. Convergence and superconvergence analysis of a new quadratic Hermite-type triangular element on anisotropic meshes[J]. Applied Mathematics and Computation, 2009, 212(1): 257-269. [20] Shi D Y, Xie P L. Morley type non-C0 nonconforming rectangular plate finite elements on anisotropic meshes[J]. Numerical Methods for Partial Differential Equations, 2010, 26(3): 723-744. [21] Shi D Y, Wang X L. Two low order characteristic finite element methods for a convection-dominated transport problem[J]. Computers and Mathematics With Applications, 2010, 59(12): 3630-3639.
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