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Partition of unity a posteriori error estimators for the linear elasticity eigenvalue problem

  • Joscha Gedicke
  • Karen Petersen
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Abstract

In this paper we consider the linear elasticity eigenvalue problem with different boundary conditions and examine two a posteriori error estimators, that compute solutions to local residual problems using a partition of unity and localized residuals. These a posteriori error estimators are known for the source problem, and in this paper we investigate their reliability and efficiency for the given eigenvalue problem with Dirichlet, Neumann and gliding boundary conditions. In numerical experiments we test the performance of the estimators on different domains, with different boundary conditions, and with different polynomial degrees. The numerical experiments show efficiency indices closer to one compared to the standard residual-based a posteriori error estimator.

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Cite

BibTeXRIS
BibTeX
@misc{gedicke2026partition,
  title = {{Partition of unity a posteriori error estimators for the linear elasticity eigenvalue problem}},
  author = {Joscha Gedicke and Karen Petersen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12865},
  eprint = {2609.12865},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12865},
}
RIS
TY  - UNPB
TI  - Partition of unity a posteriori error estimators for the linear elasticity eigenvalue problem
AU  - Joscha Gedicke
AU  - Karen Petersen
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12865
UR  - https://arxiv.org/abs/2609.12865
AB  - In this paper we consider the linear elasticity eigenvalue problem with different boundary conditions and examine two a posteriori error estimators, that compute solutions to local residual problems using a partition of unity and localized residuals. These a posteriori error estimators are known for the source problem, and in this paper we investigate their reliability and efficiency for the given eigenvalue problem with Dirichlet, Neumann and gliding boundary conditions. In numerical experiments we test the performance of the estimators on different domains, with different boundary conditions, and with different polynomial degrees. The numerical experiments show efficiency indices closer to one compared to the standard residual-based a posteriori error estimator.
ER  -