Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis Academic Article

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 {h^{1/2}} for a simple symmetric scheme, and of order h 3 / 2 {h^{3/2}} for both a nonsymmetric and a more accurate symmetric one, provided that the solution belongs to H 1 + {H^{1 + alpha }} for > 1 2 alpha > frac {1}{2} and > 3 2 alpha > frac {3}{2} , respectively.