论文期刊

Superconvergence of a stabilized finite element approximation for the Stokes equations using a local coarse mesh L2 projection




作者: Jian Li, Liquan Mei, Zhangxin Chen
发表/完成日期: 2012-01-16
期刊名称: Numerical methods for PDEs
期卷: 28(1)
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论文简介
This article first recalls the results of a stabilized finite element method based on a local Gauss integration
method for the stationary Stokes equations approximated by low equal-order elements that do not satisfy the
inf-sup condition. Then, we derive general superconvergence results for this stabilized method by using a
local coarse mesh L2 projection. These supervergence results have three prominent features. First, they are
based on a multiscale method defined for any quasi-uniform mesh. Second, they are derived on the basis of a
large sparse, symmetric positive-definite system of linear equations for the solution of the stationary Stokes
problem. Third, the finite elements used fail to satisfy the inf-sup condition. This article combines the merits
of the new stabilized method with that of the L2 projection method. This projection method is of practical
importance in scientific computation. Finally, a series of numerical experiments are presented to check the
theoretical results obtained.