A FE-MIFVE method for three-dimensional (3D) elliptic interface problems

In this paper, we propose a FE-MIFVE method for the solution of the three-dimensional elliptic interface problems on structured grids. The method uses the standard finite element discretization on regular elements, and uses the modified immersed finite volume element discretization on interface elements. By designing a suitable function which has the same jumps as the solution, we turn the original elliptic interface problem with nonhomogeneous jump conditions to be an elliptic interface problem with homogeneous jump conditions. Numerical experiments for various problems show the new proposed FE-MIFVE method can serve as an efficient field solver in a simulation on structured grids, such as predicting the electrostatics of solvated biomolecules.