Hybridized CutFEM for Elliptic Interface Problems

TL;DR

This paper introduces a hybridized cut finite element method for elliptic interface problems that allows flexible mesh coupling over internal interfaces, providing optimal error estimates and numerical validation.

Contribution

It develops a novel hybridized cut finite element approach with a Nitsche type coupling for general meshes in elliptic interface problems.

Findings

Optimal error estimates achieved

Condition number estimate for Schur complement

Numerical examples demonstrating effectiveness

Abstract

We design and analyze a hybridized cut finite element method for elliptic interface problems. In this method very general meshes can be coupled over internal unfitted interfaces, through a skeletal variable, using a Nitsche type approach. We discuss how optimal error estimates for the method are obtained using the tools of cut finite element methods and prove a condition number estimate for the Schur complement. Finally, we present illustrating numerical examples.