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On the convergence of finite-difference schemes for parabolic equations with variable coefficients

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Summary

We study the convergence of the finite-difference schemes for the first initial-boundary value problem for linear second-order parabolic equations with variable coefficients. Using the bilinear version of the Bramble-Hilbert lemma we obtain estimate of convergence, in discreteW 1, 1/22 norm, compatible with the smoothness of generalized solutionu∈W λ, λ/22 (Q) (1<λ≦3) and coefficients of equation.

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Authors and Affiliations

  1. Faculty of Sciences, Institute of Mathematics, University of Belgrade, Studentski trg 16, P.B. 550, YU-11000, Belgrade, Yugoslavia

    Boško S. Jovanović

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  1. Boško S. Jovanović
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Jovanović, B.S. On the convergence of finite-difference schemes for parabolic equations with variable coefficients. Numer. Math. 54, 395–404 (1989). https://doi.org/10.1007/BF01396321

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  • DOI: https://doi.org/10.1007/BF01396321

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