Geodesic
Finite Difference Approximation of a Parabolic Problem with Variable Coefficients
Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 49 .

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We study the convergence of a finite difference scheme that approximates the third initial-boundary-value 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 second-order 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.
Classification : 65M15
Keywords: parabolic initial-boundary-value problem, oblique derivative boundary condition, finite differences, Sobolev spaces, convergence rate estimates 
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     title = {Finite {Difference} {Approximation} of a {Parabolic} {Problem} with {Variable} {Coefficients}},
     journal = {Publications de l'Institut Math\'ematique},
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Boško S. Jovanović; Zorica Milovanović. Finite Difference Approximation of a Parabolic Problem with Variable Coefficients. Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 49 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a2/