Nonconforming $hp$-FE/BE coupling on unstructured meshes based on Nitsche's method
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866917401384189952 |
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| author | Chernov, Alexey Hansbo, Peter Schetzke, Erik Marc |
| author_facet | Chernov, Alexey Hansbo, Peter Schetzke, Erik Marc |
| contents | We construct and analyse a $hp$-FE/BE coupling on non-matching meshes, based on Nitsche's method. Both the mesh size and the polynomial degree are changed to improve accuracy. Nitsche's method leads to a positive definite formulation, thus, unlike the mortar method, it does not require the Babuška-Brezzi condition for stability. The method is stable provided the stabilization function is larger than a certain threshold. We obtain an explicit bound for the threshold and derive a priori error estimates. Our analysis can be easily extended to the pure FE or the pure BE decomposition as well as to the case of more than two subdomains. The problem in a bounded domain is considered in detail, but the case of an unbounded BE subdomain and a bounded FE subdomain follows with similar arguments. We develop convergence analysis and provide numerical examples for quasi-uniform as well as geometrically refined $hp$ discretisations in both subdomains with analytic and singular solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10600 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonconforming $hp$-FE/BE coupling on unstructured meshes based on Nitsche's method Chernov, Alexey Hansbo, Peter Schetzke, Erik Marc Numerical Analysis 65N30 (Primary), 65N38 (Secondary), 65N12 We construct and analyse a $hp$-FE/BE coupling on non-matching meshes, based on Nitsche's method. Both the mesh size and the polynomial degree are changed to improve accuracy. Nitsche's method leads to a positive definite formulation, thus, unlike the mortar method, it does not require the Babuška-Brezzi condition for stability. The method is stable provided the stabilization function is larger than a certain threshold. We obtain an explicit bound for the threshold and derive a priori error estimates. Our analysis can be easily extended to the pure FE or the pure BE decomposition as well as to the case of more than two subdomains. The problem in a bounded domain is considered in detail, but the case of an unbounded BE subdomain and a bounded FE subdomain follows with similar arguments. We develop convergence analysis and provide numerical examples for quasi-uniform as well as geometrically refined $hp$ discretisations in both subdomains with analytic and singular solutions. |
| title | Nonconforming $hp$-FE/BE coupling on unstructured meshes based on Nitsche's method |
| topic | Numerical Analysis 65N30 (Primary), 65N38 (Secondary), 65N12 |
| url | https://arxiv.org/abs/2604.10600 |