Finite Difference Approximation for Parabolic Interface Problem With Time-Dependent Coefficients

Bratislav V. Sredojević, Dejan R. Bojović

The convergence of difference scheme for 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 $\widetilde{W}^{1,1/2}_2$ Sobolev norm, compatible with the smoothness of the coefficients and solution, is proved.