A Partially Penalised Immersed Finite Element Method for Elliptic Interface Problems with Non-Homogeneous Jump Conditions

Abstract

A partially penalised immersed finite element method for interface problems with discontinuous coefficients and non-homogeneous jump conditions based on unfitted meshes independent of the interface is proposed. The arising systems of linear equations have symmetric positive definite matrices which allows the use of fast solvers and existing codes. Optimal error estimates in an energy norm are derived. Numerical examples demonstrate the efficiency of the method.