On convergence of block centered finite differences for elliptic problems. (English) Zbl 0644.65062

The authors consider linear selfadjoint elliptic problems with Neumann boundary conditions in rectangular domains. It is demonstrated that, with sufficiently smooth data, the discrete L 2-norm errors for tensor product block-centered finite differences in both the approximate solution and its first derivatives are second-order for all nonuniform grids. Extensions to nonselfadjoint and parabolic problems are discussed. Computational results are presented which demonstrate the second-order convergence predicted by the theory.
Reviewer: P.Onumanyi


65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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