LOCAL REFINEMENT TECHNIQUES FOR ELLIPTIC PROBLEMS ON CELL-CENTERED GRIDS .1. ERROR ANALYSIS

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 H-1-norm are derived of order h1/2 for a simple symmetric scheme, and of order h3/2 for both a nonsymmetric and a more accurate symmetric one, provided that the solution belongs to H-1+alpha for alpha > 1/2 and alpha > 3/2, respectively.