An Immersed Weak Galerkin Method For Elliptic Interface Problems

TL;DR

This paper introduces an immersed weak Galerkin method for second-order elliptic interface problems that allows for non-aligned meshes, simplifying computations for complex geometries and demonstrating reliable accuracy and performance.

Contribution

The paper develops a novel immersed weak Galerkin method that works with uniform Cartesian meshes for complex interface problems, without requiring mesh-interface alignment.

Findings

Proves existence and uniqueness of the numerical solution

Establishes error estimates in the energy norm

Numerical results confirm the method's effectiveness

Abstract

In this paper, we present an immersed weak Galerkin method for solving second-order elliptic interface problems. The proposed method does not require the meshes to be aligned with the interface. Consequently, uniform Cartesian meshes can be used for nontrivial interfacial geometry. We show the existence and uniqueness of the numerical algorithm, and prove the error estimates for the energy norm. Numerical results are reported to demonstrate the performance of the method.