Local refinement techniques for elliptic problems on cell-centered grids. I. 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 {H^1} -norm are derived of order h 1 / 2 {h1/2} for a simple symmetric scheme, and of order h 3 / 2 {h3/2} for both a nonsymmetric and a more accurate symmetric one, provided that the solution belongs to H 1 + α {H1 + α} for α > 1 2 α > 1/2 and α > 3 2 α > 3/2 , respectively.