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Some convergence rate estimates for finite difference schemes. (English) Zbl 0949.65110

The authors use function space interpolation to prove some convergence rate estimates for finite difference schemes. They concentrate on a Dirichlet boundary value problem for a second-order linear elliptic equation with variable coefficients in the unit 3-dimensional cube. It is assumed that the solution to the problem and the coefficients of the equation belong to corresponding Sobolev spaces.

MSC:

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N06 Finite difference methods for boundary value problems involving PDEs
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