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PreprintarXiv licencearXiv

Morley element for the linear strain gradient elasticity problem

  • Xiao Li
  • Shudan Tian
  • Hua Wang
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Abstract

We establish a discrete H1-Korn inequality for finite element spaces satisfying a second order weak continuity condition. This implies that classical H2-nonconforming elements satisfy the discrete Korn inequality. Based on this result, we develop a stabilized Morley finite element method for linear strain gradient elasticity using only piecewise quadratic polynomials. Thanks to the discrete H1-Korn inequality, this method does not require any penalty parameter. We prove that the method is robust with respect to both λ and ι. Numerical experiments confirm the theoretical results.

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Cite

BibTeXRIS
BibTeX
@misc{li2026morley,
  title = {{Morley element for the linear strain gradient elasticity problem}},
  author = {Xiao Li and Shudan Tian and Hua Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24340},
  eprint = {2609.24340},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24340},
}
RIS
TY  - UNPB
TI  - Morley element for the linear strain gradient elasticity problem
AU  - Xiao Li
AU  - Shudan Tian
AU  - Hua Wang
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24340
UR  - https://arxiv.org/abs/2609.24340
AB  - We establish a discrete H^1-Korn inequality for finite element spaces satisfying a second order weak continuity condition. This implies that classical H^2-nonconforming elements satisfy the discrete Korn inequality. Based on this result, we develop a stabilized Morley finite element method for linear strain gradient elasticity using only piecewise quadratic polynomials. Thanks to the discrete H^1-Korn inequality, this method does not require any penalty parameter. We prove that the method is robust with respect to both λ and ι. Numerical experiments confirm the theoretical results.
ER  -