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arXiv · 2312.16541

Analysis of the Crouzeix-Raviart Surface Finite Element Method for vector-valued Laplacians

Carolin Mehlmann
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Abstract

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.

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Carolin Mehlmann. 2023-12-27. Analysis of the Crouzeix-Raviart Surface Finite Element Method for vector-valued Laplacians. https://arxiv.org/abs/2312.16541

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