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Numerical approximation of a two-dimensional parabolic time-dependent problem containing a delta function. (English) Zbl 1291.65256

Summary: 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 \(\widetilde{W}_2^{2, 1}\) Sobolev norm, compatible with the smoothness of the coefficients and the solution, is proved.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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