Towards a unified analysis of mixed methods for elasticity with weakly symmetric stress

We propose a framework for unified analysis of mixed methods for elasticity with weakly symmetric stress. Based on a commuting diagram in the weakly symmetric elasticity complex and extending a previous stability result, stable mixed methods are obtained by combining Stokes stable and elasticity sta...

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Bibliographic Details
Published in:Advances in computational mathematics 2016-04, Vol.42 (2), p.361-376
Main Author: Lee, Jeonghun J.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
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Summary:We propose a framework for unified analysis of mixed methods for elasticity with weakly symmetric stress. Based on a commuting diagram in the weakly symmetric elasticity complex and extending a previous stability result, stable mixed methods are obtained by combining Stokes stable and elasticity stable finite elements. We show that the framework can be used to analyze most existing mixed methods for the linear elasticity problem with elementary techniques. We also show that some new stable mixed finite elements are obtained.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-015-9427-y