An interior a priori estimate for parabolic difference operators and an application
Author:
Magnus Bondesson
Journal:
Math. Comp. 25 (1971), 4358
MSC:
Primary 65.68
MathSciNet review:
0290598
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Abstract: A general class of finitedifference approximations to a parabolic system of differential equations in a bounded domain is considered. It is shown that if a solution of the discrete problem converges in a discrete norm to a solution U of the continuous problem as the mesh size h tends to zero, then the difference quotients of converge to the corresponding derivatives of U, the convergence being uniform on any compact subset of . In particular, converges uniformly on compact subsets to U as h tends to zero, provided there is convergence in the discrete norm. The main part of the paper is devoted to the establishment of an a priori estimate for the solutions of the discrete problem. This estimate is then used to derive the stated result.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197102905989
PII:
S 00255718(1971)02905989
Keywords:
Parabolic difference operator,
a priori estimate,
boundary value problem,
convergence in maximum norm,
convergence of difference quotients
Article copyright:
© Copyright 1971 American Mathematical Society
