Bulk-Surface Coupled PDE with an Open Boundary
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918462286200832 |
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| author | Epstein, Charles L. Mori, Yoichiro Zhou, Han |
| author_facet | Epstein, Charles L. Mori, Yoichiro Zhou, Han |
| contents | We study a bulk-surface coupled Laplace system involving an embedded open boundary. The problem is reformulated as an integro-differential equation using boundary integral representations, for which we establish existence and uniqueness of the solution. A Wiener-Hopf technique is employed to study the solution regularity and derive asymptotic expressions for the edge singularity. Building on these results, we develop a finite element method that incorporates the singularity structure and provide a rigorous error analysis. Numerical experiments confirm the theoretical convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20798 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bulk-Surface Coupled PDE with an Open Boundary Epstein, Charles L. Mori, Yoichiro Zhou, Han Numerical Analysis Analysis of PDEs We study a bulk-surface coupled Laplace system involving an embedded open boundary. The problem is reformulated as an integro-differential equation using boundary integral representations, for which we establish existence and uniqueness of the solution. A Wiener-Hopf technique is employed to study the solution regularity and derive asymptotic expressions for the edge singularity. Building on these results, we develop a finite element method that incorporates the singularity structure and provide a rigorous error analysis. Numerical experiments confirm the theoretical convergence rates. |
| title | Bulk-Surface Coupled PDE with an Open Boundary |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2604.20798 |