Variational-difference method for estimation of electrical durability of dielectrics

The electrostatical boundary-value problem (BVP) for a dielectric in powerful electric field is formulated as the variational problem with taking into account of polarization saturation and current of conductivity. The existence of external charges with no solution of electrostatical BVP is proved. It is treated as beginning of the electric puncture of dielectric. For estimation of puncture conditions the limiting analysis problem (LAP) is formulated. The solution of this original variational problem belongs to the space of scalar functions with bounded variations. As a result, LAP needs a relaxation. The partial relaxation is proposed. It is based on the special discontinuous finite-element approximation. Numerical results show that for solving LAP the proposed technique has the qualitative advantage over the standard continuous finite-element approximation.