Analysis of a Discontinuous Galerkin Method for Diffusion Problems on Intersecting Domains
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918245510938624 |
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| author | Kuchta, Miroslav Masri, Rami Riviere, Beatrice |
| author_facet | Kuchta, Miroslav Masri, Rami Riviere, Beatrice |
| contents | The interior penalty discontinuous Galerkin method is applied to solve elliptic equations on either networks of segments or networks of planar surfaces, with arbitrary but fixed number of bifurcations. Stability is obtained by proving a discrete Poincaré's inequality on the hypergraphs. Convergence of the scheme is proved for $H^r$ regularity solution with $1 < r \leq 2$. In the low regularity case ($r \leq 3/2$), a weak consistency result is obtained via generalized lifting operators for Sobolev spaces defined on hypergraphs. Numerical experiments confirm the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of a Discontinuous Galerkin Method for Diffusion Problems on Intersecting Domains Kuchta, Miroslav Masri, Rami Riviere, Beatrice Numerical Analysis 65M60, 65N30, 53Z99, 57N99 The interior penalty discontinuous Galerkin method is applied to solve elliptic equations on either networks of segments or networks of planar surfaces, with arbitrary but fixed number of bifurcations. Stability is obtained by proving a discrete Poincaré's inequality on the hypergraphs. Convergence of the scheme is proved for $H^r$ regularity solution with $1 < r \leq 2$. In the low regularity case ($r \leq 3/2$), a weak consistency result is obtained via generalized lifting operators for Sobolev spaces defined on hypergraphs. Numerical experiments confirm the theoretical results. |
| title | Analysis of a Discontinuous Galerkin Method for Diffusion Problems on Intersecting Domains |
| topic | Numerical Analysis 65M60, 65N30, 53Z99, 57N99 |
| url | https://arxiv.org/abs/2512.11111 |