Discontinuous Galerkin Immersed Finite Element Methods for Parabolic Interface Problems

TL;DR

This paper develops and analyzes interior penalty discontinuous Galerkin methods with immersed finite element functions to effectively solve parabolic interface problems, demonstrating optimal convergence through theoretical proofs and numerical validation.

Contribution

It introduces novel interior penalty discontinuous Galerkin schemes with immersed finite element functions for parabolic interface problems, providing rigorous convergence analysis.

Findings

Optimal convergence rates established for semi-discrete schemes

Optimal convergence rates established for fully discrete schemes

Numerical experiments confirm theoretical results

Abstract

In this article, interior penalty discontinuous Galerkin methods using immersed finite element functions are employed to solve parabolic interface problems. Typical semi-discrete and fully discrete schemes are presented and analyzed. Optimal convergence for both semi-discrete and fully discrete schemes are proved. Some numerical experiments are provided to validate our theoretical results.