Finite difference approximations for some interface problems with variable coefficients
The authors investigate a general elliptic interface problem in two variables, in a rectangular domain, crossed by a curvilinear interface. By a suitable variable change, the problem is transformed into an analogous one with a rectilinear interface. For this new interface problem, a finite difference scheme is proposed. Also, the case of a parabolic initial boundary value problem is considered and two finite difference schemes, one implicit and one explicit, for its numerical solution, are proposed. The interface problems are treated in the sense of distributions. Convergence rate estimates in discret Sobolev norms and some abstract stability results are obtained. To improve the efficiency of the proposed implicit scheme for the initial boundary value problem of parabolic type ( because a discrete elliptic problem has to be solved at every time level), the authors develop in the last section an efficient factorized unconditionally stable finite difference scheme. No numerical illustration are made.
elliptic and parabolic interface problems
scientific article; zbMATH DE number 5500865
scientific article