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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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An analysis of a uniformly convergent finite difference/finite element scheme for a model singular-perturbation problem
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by Eugene C. Gartland PDF
Math. Comp. 51 (1988), 93-106 Request permission

Abstract:

Uniform $\mathcal {O}({h^2})$ convergence is proved for the El-Mistikawy-Werle discretization of the problem $- \varepsilon u”+ au’+ bu = f$ on (0,1), $u(0) = A$, $u(1) = B$, subject only to the conditions $a,b,f \in {\mathcal {W}^{2,\infty }}[0,1]$ and $a(x) > 0, 0 \leq x \leq 1$. The principal tools used are a certain representation result for the solutions of such problems that is due to the author [Math. Comp., v. 48, 1987, pp. 551-564] and the general stability results of Niederdrenk and Yserentant [Numer. Math., v. 41, 1983, pp. 223-253]. Global uniform $\mathcal {O}(h)$ convergence is proved under slightly weaker assumptions for an equivalent Petrov-Galerkin formulation.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 93-106
  • MSC: Primary 65L10; Secondary 65L60
  • DOI: https://doi.org/10.1090/S0025-5718-1988-0942145-6
  • MathSciNet review: 942145