The optimal convergence rate of a C1 finite element method for non-smooth domains

被引：5

作者：

Soane, Ana Maria ^{[2
]}

Suri, Manil ^{[1
]}

Rostamian, Rouben ^{[1
]}

机构：

[1] UMBC, Dept Math & Stat, Baltimore, MD 21250 USA

[2] Politecn Milan, Dipartimento Matemat F Brioschi, MOX, I-20133 Milan, Italy

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 233卷 / 10期

关键词：

Finite elements; Non-convex polygonal domains; Corner singularities; Graded meshes; Optimal convergence rates; WEIGHTED REGULARIZATION; MAXWELL EQUATIONS;

D O I：

10.1016/j.cam.2009.11.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish optimal (up to arbitrary epsilon > 0) convergence rates for a finite element formulation of a model second order elliptic boundary value problem in a weighted H-2 Sobolev space with 5th degree Argyris elements. This formulation arises while generalizing to the case of non-smooth domains an unconditionally stable scheme developed by Liu et al. [J.-G. Liu, J. Liu, R.L. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Comm. Pure Appl. Math. 60 (2007) pp. 1443-1487] for the Navier-Stokes equations. We prove the optimality for both quasiuniform and graded mesh refinements, and provide numerical results that agree with our theoretical predictions. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：2711 / 2723

页数：13

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