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A local superconvergence analysis of the finite element method for the Stokes equations by local projections

✍ Scribed by Jian Li; Yinnian He; Jianhua Wu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
274 KB
Volume
74
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, we focus on a local superconvergence analysis of the finite element method for the Stokes equations by local projections. The local and global superconvergence results of finite element solutions are provided for the Stokes problem under some corresponding regularity assumptions. Conclusion can be drawn that the local superconvergence has advantages over the global superconvergence in two important aspects. On the one hand, it offsets theoretical limitation in practical applications. On the other hand, interior estimates are derived on the base of local properties of the domain without global smoothness for the exact solution and prior regularity of the problem globally over the whole domain.

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