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

✍ Scribed by Jian Li; Liquan Mei; Zhangxin Chen

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 488 KB
• Volume: 28
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.20610

✦ Synopsis

Abstract

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 L^2^ 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 L^2^ 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. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 28: 115‐126, 2012