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Quadratic convergence for cell-centered grids. (English) Zbl 0651.65086
Rectangular cell-centered finite difference approximations of a plane pressure-flow equation in a rectangular region with no-flow conditions at the boundary are considered. Despite a formal inconsistency in the finite difference equations, due to the use of cell-centered rather than point- distributed grids, it is shown that the solution errors are $O(h\sp 2)$ when the mesh width $h\to 0$. The methods are quite elementary and rely upon an explicit treatment of truncation error terms which are not $O(h\sp 2)$.
Reviewer: S.L.Svensson

##### MSC:
 65Z05 Applications of numerical analysis to physics 65N15 Error bounds (BVP of PDE) 65N50 Mesh generation and refinement (BVP of PDE) 76S05 Flows in porous media; filtration; seepage
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