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1. Error estimates for finite difference solutions of second-order elliptic equations in discrete Sobolev spaces

Author

Doh, Hyun Soo

Subjects
Finite difference approximations, lp error estimates
Abstract

We derive a priori lp-estimates for nite difference solutions of second-order elliptic equations with continuous coefficients in the whole space. We shall mainly use the Fefferman-Stein theorem and discrete Sobolev inequalities to establish our purpose. Based on these lp-estimates, we obtain the convergence rate of the approximate solutions and their difference quotients in the sup norm.

Published
2012

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