A Priori Error Estimates for Some Discontinuous Galerkin Immersed Finite Element Methods

摘要

In this paper, we derive a priori error estimates for a class of interiorpenalty discontinuous Galerkin (DG) methods using immersed finite element (IFE)functions for a classic second-order elliptic interface problem. The errorestimation shows that these methods can converge optimally in a mesh-dependentenergy norm. The combination of IFEs and DG formulation in these methods allowslocal mesh refinement in the Cartesian mesh structure for interface problems.Numerical results are provided to demonstrate the convergence and local meshrefinement features of these DG-IFE methods.