"On the Sharpness of a Korn’s Inequality for Piecewise H1 Space and its" by Qingguo Hong, Young Ju Lee et al.
 

Abstract

In this paper, we investigate the sharpness of a Korn's inequality for piecewise H1 space and its applications. We first revisit a Korn's inequality for the piecewise H1 space based on general polygonal or polyhedral decompositions of the domain. We express the Korn's inequality with minimal jump terms. Then we prove that such minimal jump conditions are sharp for achieving the Korn's inequality. The sharpness of the Korn's inequality and explicitly given minimal conditions can be used to test whether any given finite element spaces satisfy Korn's inequality, immediately as well as to build or modify nonconforming finite elements for Korn's inequality to hold.

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant NSF DMS-2419033

Keywords and Phrases

Korn's inequality; Piecewise space; Sharpness

International Standard Serial Number (ISSN)

1573-7691; 0885-7474

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2025 Springer, All rights reserved.

Publication Date

01 Jan 2025

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