An unfitted Hybrid High-Order method for elliptic interface problems

TL;DR

This paper introduces a novel unfitted Hybrid High-Order method for elliptic interface problems, capable of handling complex interfaces and material contrasts with proven stability and optimal error estimates.

Contribution

It presents a new unfitted HHO method using Nitsche-type formulation, supporting polyhedral meshes and ensuring robustness against interface cuts and material contrasts.

Findings

Proves stability and optimal error estimates in the $H^1$-norm.

Demonstrates robustness with respect to interface cuts and material contrast.

Supports complex interface geometries on unfitted meshes.

Abstract

We design and analyze a Hybrid High-Order (HHO) method on unfitted meshes to approximate elliptic interface problems. The curved interface can cut through the mesh cells in a very general fashion. As in classical HHO methods, the present unfitted method introduces cell and face unknowns in uncut cells, but doubles the unknowns in the cut cells and on the cut faces. The main difference with classical HHO methods is that a Nitsche-type formulation is used to devise the local reconstruction operator. As in classical HHO methods, cell unknowns can be eliminated locally leading to a global problem coupling only the face unknowns by means of a compact stencil. We prove stability estimates and optimal error estimates in the $H^1$-norm. Robustness with respect to cuts is achieved by a local cell-agglomeration procedure taking full advantage of the fact that HHO methods support polyhedral meshes. Robustness with respect to the contrast in the material properties from both sides of the interface is achieved by using material-dependent weights in Nitsche's formulation.