Flux-equilibrated based a posteriori error analysis for an interface problem with CutFEM

TL;DR

This paper develops a flux-based a posteriori error estimator for elliptic interface problems solved with CutFEM, ensuring local flux recovery and conservation, with proven reliability and demonstrated effectiveness.

Contribution

It introduces a flux recovery technique within the Raviart-Thomas space for CutFEM, providing sharp reliability estimates for interface problems with discontinuous coefficients.

Findings

The error estimator is proven to be reliably sharp.

Numerical experiments confirm the effectiveness of the proposed approach.

Abstract

This paper addresses the local recovery of conservative fluxes and the a posteriori error analysis for an elliptic interface problem with discontinuous coefficients. The transmission conditions on the interface are imposed by means of Nitsche's method and the discretization is carried out using conforming finite elements on unfitted meshes via the CutFEM method. A flux is subsequently defined in the global Raviart-Thomas space, ensuring that it satisfies the natural conservation property on the cut cells, and is then employed in the a posteriori error analysis. We prove here the sharp reliability of the error estimator and show a numerical experiment which illustrates the approach.