Numerical analysis of a generalized diffuse interface model for the electrical breakdown process

The subject of the present work is a previously suggested generalization of a diffuse interface model describing the development of an electrical breakdown channel in a solid dielectric. Numerical analysis for the model is performed. In the analysis, the stationary distribution of the phase field is found in several characteristic cases of the problem. A modification of the finite volume method is applied so that the numerical scheme is available for determining the boundary conditions at sets of higher codimension in three-dimensional space. At that the solution function is expected to have a singularity at the points of these sets.