FINITE DIFFERENCE APPROXIMATION FOR PARABOLIC INTERFACE PROBLEM WITH TIME-DEPENDENT COEFFICIENTS

Bratislav V. Sredojevic, Dejan R. Bojovic

Abstract: 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.

Keywords: interface problem; convergence; Sobolev norm

Classification (MSC2000): 65M12; 65M15

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