An accurate finite element method for elliptic interface problems

TL;DR

This paper introduces a finite element method for elliptic interface problems with discontinuous coefficients, allowing for non-adapted meshes and achieving optimal convergence rates, validated through numerical tests.

Contribution

The paper presents a novel nonconforming finite element method that handles discontinuities along smooth curves without requiring mesh adaptation.

Findings

Achieves optimal convergence rate in the H^1-norm.

Handles meshes not aligned with the discontinuity.

Numerical tests confirm theoretical convergence.

Abstract

A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the discontinuity line. The (nonconforming) finite element space is enriched with local basis functions. We prove an optimal convergence rate in the $H^1$--norm. Numerical tests confirm the theoretical results.