Abstract

In this work we use function space interpolation to prove some convergence rate estimates for finite difference schemes. We concentrate on a Dirichlet boundary value problem for a second-order linear elliptic equation with variable coefficients in the unit 3-dimensional cube. We assume that the solution to the problem and the coefficients of the equation belong to corresponding Sobolev spaces.

Keywords: Boundary Value Problems (BVP), Finite Difference Schemes (FDS), Sobolev Spaces, Interpolation of Function Spaces, Convergence Rate Estimates.

MSC: 65N15, 46B70

Pages:  249--256     

Volume  49 ,  Issue  3$-$4 ,  1997