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

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.

arXiv comment21 pages, 15 tables, 8 figures