ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 Mathematical Subject Classification: 65 Jovanović, Boško, University of Belgrade, Yugoslavia Finite difference schemes on nonuniform meshes. Nonuniform meshes are often used for approximation of problems with generalized solutions. In this case, the order of local approximation is usually reduced. In many papers it is shown that the accuracy of the finite difference schemes can be increased using approximation of the considered differential equation in some non–mesh points. In this paper the convergence of such finite difference schemes is proved in discrete L_{2} and W_{2}^{1} norms assuming that the generalized solution of the considered boundary value problem belongs to the corresponding Sobolev space. Obtained convergence rate estimates are consistent with the smoothness of the solution of boundary value problem. Special attention is given to the multidimensional problems and to the problems with variable coefficients.