Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis
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A finite difference technique on rectangular cell-centered grids with local refinement is proposed in order to derive discretizations of second-order elliptic equations of divergence type approximating the so-called balance equation. Error estimates in a discrete -norm are derived of order for a simple symmetric scheme, and of order for both a nonsymmetric and a more accurate symmetric one, provided that the solution belongs to for and , respectively.