Analysis of the Crouzeix-Raviart Surface Finite Element Method for vector-valued Laplacians
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914154581852160 |
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| author | Mehlmann, Carolin |
| author_facet | Mehlmann, Carolin |
| contents | Recently, a nonconforming surface finite element was developed to discretize 3d vector-valued compressible flow problems arising in climate modeling. In this contribution we derive an error analysis for this approach on a vector-valued Laplace problem, which is an important operator for fluid-equations on the surface. In our setup, the problem is approximated via edge-integration on local flat triangles using the nonconforming linear Crouzeix-Raviart element. The latter is continuous at the midpoints of the edges in each vector component. This setup is numerically efficient and straightforward to implement. For this Crouzeix-Raviart discretization we introduce interpolation estimates, derive optimal error bounds in the H1-norm and L2-norm and present an estimate for the geometric error. Numerical experiments validate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16541 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analysis of the Crouzeix-Raviart Surface Finite Element Method for vector-valued Laplacians Mehlmann, Carolin Numerical Analysis Recently, a nonconforming surface finite element was developed to discretize 3d vector-valued compressible flow problems arising in climate modeling. In this contribution we derive an error analysis for this approach on a vector-valued Laplace problem, which is an important operator for fluid-equations on the surface. In our setup, the problem is approximated via edge-integration on local flat triangles using the nonconforming linear Crouzeix-Raviart element. The latter is continuous at the midpoints of the edges in each vector component. This setup is numerically efficient and straightforward to implement. For this Crouzeix-Raviart discretization we introduce interpolation estimates, derive optimal error bounds in the H1-norm and L2-norm and present an estimate for the geometric error. Numerical experiments validate the theoretical results. |
| title | Analysis of the Crouzeix-Raviart Surface Finite Element Method for vector-valued Laplacians |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2312.16541 |