A trilinear immersed finite element method for solving the EEG forward problem

This article describes a trilinear immersed finite element method for solving the EEG forward problem, which is a 3-D elliptic interface problem in the head geometry. The method uses hexahedral Cartesian meshes independent of the interfaces between head tissues, thus avoiding the sometimes difficult task of generating geometry fitting meshes. The interfaces are represented with levelsets and the finite element space is locally modified to better approximate the discontinuities of the solution. Numerical results show that this method achieves the same accuracy than the standard linear finite element method with geometry fitting mesh.