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arXiv · 2604.20798

Bulk-surface coupled PDE with an open boundary

Charles L. Epstein·Yoichiro Mori·Han Zhou
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Abstract

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.

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Charles L. Epstein, Yoichiro Mori, Han Zhou. 2026-08-09. Bulk-surface coupled PDE with an open boundary. https://arxiv.org/abs/2604.20798

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