Publications de l'Institut Mathématique, Nouvelle Série Vol. 95[109], pp. 49–62 (2014) 

FINITE DIFFERENCE APPROXIMATION OF A PARABOLIC PROBLEM WITH VARIABLE COEFFICIENTSBosko S. Jovanovic, Zorica MilovanovicUniversity of Belgrade, Faculty of Mathematics, Belgrade, SerbiaAbstract: We study the convergence of a finite difference scheme that approximates the third initialboundaryvalue problem for parabolic equation with variable coefficients on a unit square. We assume that the generalized solution of the problem belongs to the Sobolev space $W_2^{s,s/2}$, $ s\leq 3$. An almost secondorder convergence rate estimate (with additional logarithmic factor) in the discrete $W^{1,1/2}_2$ norm is obtained. The result is based on some nonstandard a priori estimates involving fractional order discrete Sobolev norms. Keywords: parabolic initialboundaryvalue problem, oblique derivative boundary condition, finite differences, Sobolev spaces, convergence rate estimates Classification (MSC2000): 65M15 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 31 Mar 2014. This page was last modified: 2 Apr 2014.
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