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

Authors: R. E. Ewing, R. D. Lazarov and P. S. Vassilevski
Journal: Math. Comp. 56 (1991), 437-461
MSC: Primary 65N06; Secondary 65N15, 65N50
MathSciNet review: 1066831
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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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Keywords: Cell-centered grid, local refinement, error estimates, elliptic problems of divergence type
Article copyright: © Copyright 1991 American Mathematical Society

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