  This work is devoted to the development of an efficient and robust technique
for accurate capturing of the electric field in multi-material problems. The
formulation is based on the finite element method enriched by the introduction
of hat-type shape function within the elements crossed by the material
interface. The peculiar feature of the proposed method consists in the direct
employment of the hat-function that requires solely one additional degree of
freedom per cut element for capturing the discontinuity in the electric
potential gradient and, thus, the electric field. This additional degree of
freedom is subsequently statically condensed element-wise prior to the assembly
of the global discrete system. As a consequence, the graph of the system matrix
remains the same as that of the standard finite element method. In order to
guarantee the robust performance of the proposed method for a wide range of
electrical material property ratios, it also accounts for the possible
discontinuities among the neighboring cut elements that arise due to employing
additional degrees of freedom fully local to the element. The method is tested
using several examples solved on structured and unstructured grids. The
proposed approach constitutes a basis for enriched FEM applicable to a wide
range of electromagnetic problems.
