Unfitted mixed finite element methods for elliptic interface problems

TL;DR

This paper introduces new unfitted mixed finite element methods for elliptic interface problems with jump coefficients, using a fictitious domain approach and distributed Lagrange multipliers, with proven stability and optimal convergence.

Contribution

It presents two novel finite element schemes with piecewise constant Lagrange multipliers, demonstrating their stability and optimal convergence through theoretical proofs and numerical validation.

Findings

Schemes are stable and converge optimally.

Numerical results confirm theoretical stability and convergence.

Applicable to fluid-structure interaction problems.

Abstract

In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our investigations is better seen when applied to the framework of fluid structure interaction problems. Two finite elements schemes with piecewise constant Lagrange multiplier are proposed and their stability is proved theoretically. Numerical results compare the performance of those elements, confirming the theoretical proofs and verifying that the schemes converge with optimal rate.