CONVERGENCE OF A MIXED FINITE ELEMENT FOR THE STOKES PROBLEM ON ANISOTROPIC MESHES

• 来源期刊: 计算数学（英文版）
• 关键词: Mixed finite element Stokes problem Anisotropic meshes Superconvergence Shape regularity assumption and inverse assumption
• 年，卷（期）: 2008,（5）
• 页码范围: 740-755
• 页数: 16页
• 语种: 英文

摘要

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works.