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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The boundary element numerical method for two-dimensional linear quadratic elliptic problems. I. Neumann control


Authors: Goong Chen and Ying-Liang Tsai
Journal: Math. Comp. 49 (1987), 479-498
MSC: Primary 65M60; Secondary 49D40, 93B40
MathSciNet review: 906183
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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 [Enhancements On Off] (What's this?)

  • [1] C. A. Brebbia, The boundary element method for engineers, Halsted Press [John Wiley & Sons], New York, 1978. MR 0502715 (58 #19652)
  • [2] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391 (16,426a)
  • [3] G. J. Fix, Survey lecture in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. Aziz and I. Babuška, eds.), Academic Press, New York, 1972.
  • [4] N. Ghosh, On the Convergence of the Boundary Element Method, Doctoral Dissertation, Dept. of Math., Cornell Univ., Ithaca, New York, 1982.
  • [5] George C. Hsiao and Wolfgang L. Wendland, A finite element method for some integral equations of the first kind, J. Math. Anal. Appl. 58 (1977), no. 3, 449–481. MR 0461963 (57 #1945)
  • [6] J.-L. Lions, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles, Avant propos de P. Lelong, Dunod, Paris; Gauthier-Villars, Paris, 1968 (French). MR 0244606 (39 #5920)
  • [7] J. L. Lions & E. Magenes, Problèmes aux Limites Non-Homogènes et Applications, Vol. I, Dunod, Paris, 1968.
  • [8] S. G. Mikhlin, Integral Equations, Pergamon Press, New York, 1950.
  • [9] Ivar Stakgold, Boundary value problems of mathematical physics. Vol. II, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1968. MR 0243183 (39 #4507)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1987-0906183-0
PII: S 0025-5718(1987)0906183-0
Article copyright: © Copyright 1987 American Mathematical Society