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

Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S.

doi:10.1090/S0025-5718-1991-1066831-5

Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis
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by R. E. Ewing, R. D. Lazarov and P. S. Vassilevski PDF

Math. Comp. 56 (1991), 437-461 Request permission

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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