Weiser, Alan; Wheeler, Mary Fanett On convergence of block centered finite differences for elliptic problems. (English) Zbl 0644.65062 SIAM J. Numer. Anal. 25, No. 2, 351-375 (1988). 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 Cited in 1 ReviewCited in 155 Documents MSC: 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs Keywords:block-centered grids; cell-centered grids; vertex-centered grids; Neumann problem; numerical examples; superconvergence; linear selfadjoint elliptic problems; tensor product block-centered finite differences; nonuniform grids × Cite Format Result Cite Review PDF Full Text: DOI