A nonconforming immersed finite element method for elliptic interface problems

TL;DR

This paper introduces a novel nonconforming immersed finite element method for elliptic interface problems with discontinuous coefficients, achieving improved error estimates and validated by numerical experiments.

Contribution

It develops a new IFE space based on rotated Q1 elements without penalty stabilization, enhancing accuracy for elliptic interface problems.

Findings

Error estimates in energy norm better than O(h√|log h|)

Error estimates in L2 norm better than O(h^2|log h|)

Numerical results confirm theoretical analysis

Abstract

A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated Q1 nonconforming finite elements with the integral-value degrees of freedom. The standard nonconforming Galerkin method is employed in this IFE method without any penalty stabilization term. Error estimates in energy and L2 norms are proved to be better than $O(h\sqrt{|\log h|})$ and $O(h^2|\log h|)$, respectively, where the logarithm factors reflect jump discontinuity. Numerical results are reported to confirm our analysis.