Uniform Superconvergence of a Finite Element Method with Edge Stabilization for Convection-Diffusion Problems

在现在的纸，边稳定技术在联合起来的平方上与指数的边界层被用于一个传送对流散开问题，用有在层区域的双线性的有限元素和网孔的粗糙的部分上的线性元素的一个 Shishkin 网孔。错误界限为 || u 被证明 - u [h ]||[E ] ，在 u 是答案 u 的某 interpolant 的地方并且哦分离答案。这 supercloseness 结果关于 L 暗示最佳的错误估计[2 ] 标准并且为改进分离答案打开门到 postprocessing 的申请。[从作者抽象]

[1]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[2]  G. I. SHISHKIN,et al.  Grid approximation of singularly perturbed elliptic equations in case of limit zero-order equations degenerating at the boundary , 1990 .

[3]  P. Hansbo,et al.  Edge stabilization for Galerkin approximations of convection?diffusion?reaction problems , 2004 .

[4]  Zhimin Zhang,et al.  Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems , 2003, Math. Comput..

[5]  Torsten Linß,et al.  Uniform superconvergence of a Galerkin finite element method on Shishkin‐type meshes , 2000 .

[6]  Lutz Tobiska,et al.  The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy , 2003, SIAM J. Numer. Anal..

[7]  Martin Stynes,et al.  A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem☆ , 1997 .

[8]  Sebastian Franz.  Continuous interior penalty method on a Shishkin mesh for convection-diffusion problems with characteristic boundary layers , 2008 .

[9]  Torsten Linß,et al.  Asymptotic Analysis and Shishkin-Type Decomposition for an Elliptic Convection–Diffusion Problem , 2001 .

[10]  Erik Burman,et al.  A Unified Analysis for Conforming and Nonconforming Stabilized Finite Element Methods Using Interior Penalty , 2005, SIAM J. Numer. Anal..

[11]  Torsten Lin,et al.  Layer-adapted meshes for convection-diusion problems , 2003 .

[12]  Roland Becker,et al.  Optimal control of the convection-diffusion equation using stabilized finite element methods , 2007, Numerische Mathematik.

[13]  Hans-Görg Roos,et al.  A Priori Estimates for the Solution of Convection-Diffusion Problems and Interpolation on Shishkin Meshes , 1997 .

[14]  G. Lube,et al.  Local projection stabilization for incompressible flows: equal-order vs. inf-sup stable interpolation. , 2008 .

[15]  Jens Markus Melenk,et al.  hp-Finite Element Methods for Singular Perturbations , 2002 .

[16]  T. Apel.  Anisotropic Finite Elements: Local Estimates and Applications , 1999 .

[17]  Torsten Linß,et al.  Layer-adapted meshes for convection-diffusion problems , 2003 .

[18]  Erik Burman,et al.  Weighted error estimates of the continuous interior penalty method for singularly perturbed problems , 2008 .

[19]  U MartinStynes.  A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem , 1997 .

[20]  M. Stynes,et al.  Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems , 1996 .

[21]  V. Thomée,et al.  The stability in _{} and ¹_{} of the ₂-projection onto finite element function spaces , 1987 .

[22]  Torsten Linß,et al.  Numerical methods on Shishkin meshes for linear convection-diffusion problems , 2001 .