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

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

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2012-08

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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.

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University of Minnesota Ph.D. dissertatation. August 2012. Major:Mathematics. Advisor: Nicolai V. Krylov. 1 computer file (PDF); ii, 60 pages.

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Doh, Hyun Soo. (2012). Error estimates for finite difference solutions of second-order elliptic equations in discrete Sobolev spaces. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/141670.

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