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# Local Refinement Techniques for Elliptic Problems on Cell-Centered Grids I. Error Analysis

R. E. Ewing, R. D. Lazarov and P. S. Vassilevski
Mathematics of Computation
Vol. 56, No. 194 (Apr., 1991), pp. 437-461
DOI: 10.2307/2008390
Stable URL: http://www.jstor.org/stable/2008390
Page Count: 25
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## Abstract

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

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