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L ∞-Error estimate for an approximation of a parabolic variational inequality

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Summary

Almost optimalL ∞-convergence of an approximation of a variational inequality of parabolic type is proved under regularity assumptions which are met by the solution of a one phase Stefan problem. The discretization employs piecewise linear finite elements in space and the backward Euler scheme in time. By means of a maximum principle the problem is reduced to an error estimate for an auxiliary parabolic equation. The latter bound is obtained by using the smoothing property of the Galerkin method.

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  1. Mathematisches Seminar der Landwirtschaftlichen Fakultät der Universität Bonn, Nußallee 15, D-5300, Bonn 1, Germany

    Alfredo Fetter

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  1. Alfredo Fetter
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Fetter, A. L ∞-Error estimate for an approximation of a parabolic variational inequality. Numer. Math. 50, 557–565 (1987). https://doi.org/10.1007/BF01408576

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