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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 2024 MCQ for Mathematics of Computation is 1.78.

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The boundary element numerical method for two-dimensional linear quadratic elliptic problems. I. Neumann control
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by Goong Chen and Ying-Liang Tsai PDF
Math. Comp. 49 (1987), 479-498 Request permission

Abstract:

For two-dimensional distributed control systems governed by the Laplace equation, the boundary element method is an efficient numerical method to solve problems whose quadratic cost involves boundary integrals only. In this paper we formulate a duality-boundary integral equation scheme and use piecewise constant boundary elements to approximate the problem. This method involves discretization of the boundary curve only and it can conveniently handle the compatibility constraint due to the Neumann data. Convergence and optimal error estimates $\mathcal {O}(h)$ have been proved. Numerical data for the case of a disk are computed to illustrate the theory.
References
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 479-498
  • MSC: Primary 65M60; Secondary 49D40, 93B40
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0906183-0
  • MathSciNet review: 906183