Numerical analysis of dielectrics in powerful electrical fields

Abstract

The limiting analysis problem for dielectrics in nonhomogeneous powerful electrical fields is considered. In the framework of this problem the external charges for which the appropriate electrostatical variational problem has no solution are calculated, that solution is treated as a beginning of the electrical puncture of dielectric. From the mathematical point of view the limiting analysis problem is non-correct and needs a relaxation. This is achieved using a partial relaxation based on a special discontinuous finite-element approximation.