Finite Element Methods for Elastic Contact: Penalty and Nitsche
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915308787204096 |
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| author | Gustafsson, Tom Stenberg, Rolf |
| author_facet | Gustafsson, Tom Stenberg, Rolf |
| contents | We consider two methods for treating elastic contact problems with the finite element method; the penalty method and Nitsche's method. For the penalty method we discuss how the penalty parameter should be chosen. Both the theoretical analysis and numerical examples show that an optimal convergence rate cannot be achieved. The method is contrasted to that of Nitsche which is optimally convergent. We also give the derivation of Nitsche's method by a very simple consistency correction of the penalty method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite Element Methods for Elastic Contact: Penalty and Nitsche Gustafsson, Tom Stenberg, Rolf Numerical Analysis We consider two methods for treating elastic contact problems with the finite element method; the penalty method and Nitsche's method. For the penalty method we discuss how the penalty parameter should be chosen. Both the theoretical analysis and numerical examples show that an optimal convergence rate cannot be achieved. The method is contrasted to that of Nitsche which is optimally convergent. We also give the derivation of Nitsche's method by a very simple consistency correction of the penalty method. |
| title | Finite Element Methods for Elastic Contact: Penalty and Nitsche |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.21776 |