Discontinuous Galerkin Immersed Finite Element Methods for Parabolic Interface Problems
It provides a theoretical foundation for solving parabolic interface problems with discontinuous Galerkin methods, but the contribution is incremental as it extends existing techniques to a new problem class.
The paper develops and analyzes discontinuous Galerkin immersed finite element methods for parabolic interface problems, proving optimal convergence for both semi-discrete and fully discrete schemes and validating them with numerical experiments.
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.