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DOE OSTI · 2341972

Generalized Korn’s inequalities for piecewise $H¹$ and $H²$ vector fields

Williams, David·Hong, Qingguo
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Abstract

The purpose of this paper is to construct a new class of discrete generalized Korn’s inequalities for piecewise $H^1$ vector fields and piecewise $H^2$ 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. Furthermore, 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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97 MATHEMATICS AND COMPUTING

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Williams, David, Hong, Qingguo. 2024-01-31. Generalized Korn’s inequalities for piecewise $H¹$ and $H²$ vector fields. https://doi.org/10.1090/mcom%2F3935

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