Work

Unfitted Hybrid High-Order Methods Stabilized by Polynomial Extension for Elliptic Interface Problems

Year: 2026

Type: article

Abstract: . In this work, we study the design and analysis of a novel hybrid high-order (HHO) method on unfitted meshes. HHO methods rely on a pair of unknowns, combining polynomials attached to the mesh faces and the mesh cells. In the unfitted framework, the interface can cut through the mesh cells in a very general fashion, and the polynomial unknowns are doubled in the cut cells and the cut faces. In order to avoid the ill-conditioning issues caused by the presence of small cut cells, the novel approach introduced herein is to use polynomial extensions in the definition of the gradient reconstruction operator. Stability and consistency results are established, leading to optimally decaying error estimates. The theory is illustrated by numerical experiments.

Source: SIAM Journal on Numerical Analysis

Authors: Erik Burman, Alexandre Ern, Romain Mottier

Institutions: University College London, Centre National de la Recherche Scientifique, CERMICS, Institut Polytechnique de Paris, Centre Inria de Paris, SERENA: Simulation for the Environment: Reliable and Efficient Numerical Algorithms, École nationale des ponts et chaussées, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, CEA DAM Île-de-France

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Funder: Engineering and Physical Sciences Research Council

Awards: Quantitative estimates of discretisation and modelling errors in variational data assimilation for incompressible flows, Computational methods for inverse problems subject to wave equations in heterogeneous media

OpenAlex ID: W4415016010

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