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arXiv · 2512.18905

Weak Galerkin finite element methods for elliptic interface problems on nonconvex polygonal partitions

Chunmei Wang·Shangyou Zhang
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Abstract

This paper proposes a weak Galerkin (WG) finite element method for elliptic interface problems defined on nonconvex polygonal partitions. The method features a built-in stabilizer and retains a simple, symmetric, and positive definite formulation. An optimal-order error estimate is rigorously derived in the discrete $H^1$ norm. Furthermore, a series of numerical experiments are provided to verify the theoretical results and to demonstrate the robustness and effectiveness of the proposed WG method for elliptic interface problems.

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Chunmei Wang, Shangyou Zhang. 2025-12-21. Weak Galerkin finite element methods for elliptic interface problems on nonconvex polygonal partitions. https://arxiv.org/abs/2512.18905

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