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 -norm are derived of order for a simple symmetric scheme, and of order for both a nonsymmetric and a more accurate symmetric one, provided that the solution belongs to for and , respectively.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1066831-5

Keywords:
Cell-centered grid,
local refinement,
error estimates,
elliptic problems of divergence type

Article copyright:
© Copyright 1991
American Mathematical Society