An adaptive high-order unfitted finite element method for elliptic interface problems

TL;DR

This paper introduces an adaptive high-order unfitted finite element method for elliptic interface problems, featuring a novel hp-domain inverse estimate and reliable error estimation, validated through numerical experiments.

Contribution

It presents a new hp-domain inverse estimate enabling stable and efficient adaptive finite element methods on Cartesian meshes for interface problems.

Findings

Stable finite element method under practical mesh conditions

Reliable a posteriori error estimates derived

Numerical examples confirm theoretical results

Abstract

We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse estimate which allows us to prove the stability of the finite element method under practical interface resolving mesh conditions and also prove the lower bound of the hp a posteriori error estimate. Numerical examples are included.