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

TL;DR

This paper introduces a weak Galerkin finite element method tailored for elliptic interface problems on nonconvex polygons, providing stability, optimal error estimates, and verified through numerical experiments.

Contribution

It presents a novel WG finite element approach with a built-in stabilizer for complex nonconvex geometries, ensuring accuracy and robustness.

Findings

Optimal error estimates in discrete H^1 norm

Method is stable and symmetric

Numerical results confirm theoretical predictions

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.