On the Convergence of Difference Scheme for Parabolic Problems with Concentrated Data

Abstract

Parabolic equations with unbounded coefficients and even generalized functions (in particular Dirac-delta functions) model large-scale of problems in the heat-mass transfer. This paper provides estimates for the convergence rate of difference scheme in discrete Sobolev like norms, compatible with the smoothness of the differential problems solutions, i.e. with the smoothness of the input data.