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.
Recommended Citation
Q. Hong et al., "On the Sharpness of a Korn’s Inequality for Piecewise H1 Space and its Applications," Journal of Scientific Computing, vol. 102, no. 1, article no. 6, Springer, Jan 2025.
The definitive version is available at https://doi.org/10.1007/s10915-024-02724-w
Department(s)
Mathematics and Statistics
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
Comments
National Science Foundation, Grant NSF DMS-2419033