An extended mixed finite element method for elliptic interface problems

TL;DR

This paper introduces an extended mixed finite element method for elliptic interface problems that achieves optimal convergence regardless of interface location, using stabilization and specific element spaces.

Contribution

It develops a stabilized mixed finite element approach with interface-independent convergence, advancing numerical solutions for elliptic interface problems.

Findings

Discrete inf-sup constant is interface-location independent

Optimal convergence achieved regardless of interface position

Numerical examples verify theoretical results

Abstract

In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, we present a mixed approximation form based on Brezzi-Douglas-Marini element space and the piecewise constant function space, and show that the discrete inf-sup constant is independent of how the interface intersects the triangulation. Furthermore, we derive that the optimal convergence holds independent of the location of the interface relative to the mesh. Finally, some numerical examples are presented to verify our theoretical results.