Extended Finite-Element Method for Weak Discontinuities in Electric Fields

In this paper, the extended finite-element method (XFEM) is used for modeling weak discontinuities in electric fields. For a weak discontinuous domain, the first-order derivative of the electric potential is discontinuous although the electric potential, degree of freedom, is continuous. In order to improve the approximation space of the conventional finite element method (CFEM), the enrichment function of the key of XFEM is used to model weak discontinuous solutions independent of the mesh. Interfaces among different materials can be described well by using the level set method. Numerical examples applied to the parallel plate electrodes in 1-D and the insulating oil with a bubble in 2-D static electric field involving error analysis, computational time, and electric field computations are provided to demonstrate the utility of XFEM in electric fields.