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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


An interior a priori estimate for parabolic difference operators and an application
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by Magnus Bondesson PDF
Math. Comp. 25 (1971), 43-58 Request permission


A general class of finite-difference approximations to a parabolic system of differential equations in a bounded domain $\Omega$ is considered. It is shown that if a solution ${U_h}$ of the discrete problem converges in a discrete ${L^2}$ norm to a solution U of the continuous problem as the mesh size h tends to zero, then the difference quotients of ${U_h}$ converge to the corresponding derivatives of U, the convergence being uniform on any compact subset of $\Omega$. In particular, ${U_h}$ converges uniformly on compact subsets to U as h tends to zero, provided there is convergence in the discrete ${L^2}$ 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
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 43-58
  • MSC: Primary 65.68
  • DOI:
  • MathSciNet review: 0290598