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arXiv · 2207.00695

Generalized Korn's Inequalities for Piecewise $H^2$ Vector Fields

David M. Williams·Qingguo Hong
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Abstract

The purpose of this paper is to construct a new class of discrete generalized Korn's inequalities for piecewise H2 vector fields in three-dimensional space. The resulting Korn's inequalities are different from the standard Korn's inequalities, as they involve the trace-free symmetric gradient operator, in place of the usual symmetric gradient operator. It is anticipated that the new generalized Korn's inequalities will be useful for the analysis of a broad range of finite element methods, including mixed finite element methods and discontinuous Galerkin methods.

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BibTeXRIS

David M. Williams, Qingguo Hong. 2022-07-02. Generalized Korn's Inequalities for Piecewise $H^2$ Vector Fields. https://arxiv.org/abs/2207.00695

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