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Convergence rates of parabolic difference schemes for non-smooth data


Authors: Vidar Thomée and Lars Wahlbin
Journal: Math. Comp. 28 (1974), 1-13
MSC: Primary 65M10
DOI: https://doi.org/10.1090/S0025-5718-1974-0341889-7
MathSciNet review: 0341889
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Abstract: Consider the approximate solution of the initial-value problem for a parabolic system by means of a parabolic finite difference scheme of accuracy $ \mu $. The main result of the present paper is essentially that for positive time and v in $ {W_1}^s$ with $ 1 < s \leq \mu $, the error in the maximum norm is $ O({h^s})$ for small mesh-widths h.


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DOI: https://doi.org/10.1090/S0025-5718-1974-0341889-7
Article copyright: © Copyright 1974 American Mathematical Society

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