Convergence rates of parabolic difference schemes for non-smooth data

Thomée, Vidar; Wahlbin, Lars

doi:10.1090/S0025-5718-1974-0341889-7

Convergence rates of parabolic difference schemes for non-smooth data
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by Vidar Thomée and Lars Wahlbin PDF

Math. Comp. 28 (1974), 1-13 Request permission

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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Linear Partial Differential Operators

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