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

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.