Numerical approximation of a two-dimensional parabolic time-dependent problem containing a delta function

摘要

The convergence of a difference scheme for a two-dimensional initial-boundary value problem for the heat equation with concentrated capacity and time-dependent coefficients of the space derivatives is considered. An estimate of the rate of convergence in a special discrete W˜22,1 Sobolev norm, compatible with the smoothness of the coefficients and the solution, is proved.