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Lagrange multipliers for higher order elliptic operators

Published online by Cambridge University Press:  15 April 2005

Carlos Zuppa
Carlos Zuppa*
Affiliation:
Departamento de Matemáticas, Universidad Nacional de San Luis, Chacabuco y Pedernera, 5700, San Luis, Argentina. zuppa@unsl.edu.ar
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Abstract

In this paper, the Babuška's theory of Lagrange multipliers is extended to higher order elliptic Dirichlet problems. The resulting variational formulation provides an efficient numerical squeme in meshless methods for the approximation of elliptic problems with essential boundary conditions.

Keywords

Elliptic operatorsDirichlet boundary-value problemLagrange multipliers.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 2 , March 2005 , pp. 419 - 429
Copyright
© EDP Sciences, SMAI, 2005

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References

S. Agmon, Lectures on elliptic boundary value problems. D. Van Nostrand, Princeton, N. J. (1965).
I. Babuška, The finite element method with lagrange multipliers. Numer. Math. 20 (1973) 179–192.
I. Babuška and A.K. Aziz, Survey lectures on the mathematical foundations of the finite element method, The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations. Academic Press, New York (1972) 5–359.
Belytschko, T., Krongauz, Y.. D. Organ, M. Fleming and P. Krysl, Meshless methods: an overview and recent development. Comput. Methods Appl. Mech. Engrg. 139 (1996a) 3–47. CrossRef
J.M. Berezanskii, Expansions in Eigenfunctions of Self-Adjoint Operators, Translations of Mathematical Monographs 17, American Mathematical Society, Providence, R.I. (1968).
S.C. Brener and L.R. Scott, The mathematical theory of finite elements methods. Springer-Verlag, New York (1994).
C.A. Duarte and J.T. Oden, H-p clouds - an h-p meshless method. Num. Methods Partial Differential Equations. 1 (1996) 1–34.
S. Li and W.K. Liu, Meshfree and particle methods and their applications. Applied Mechanics Reviews (ASME) (2001).
J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Dunod, Paris (1968).
G.R. Liu, Mesh Free Methods: Moving Beyond the Finite Element Method. CRC Press, Boca Raton, USA (2002).
J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967).
J.T. Oden and J.N. Reddy, An introduction to the mathematical theory of finite elements. Wiley Interscience, New York (1976).
K.T. Smith, Inequalities for formally positive integro-differential forms. Bull. Amer. Math. Soc. 67 (1961) 368–370.
Volevič, L.R., Solvability of boundary value problems for general elliptic systems. Amer. Math. Soc. Transl. 67 (1968) 182–225.
C. Zuppa, G. Simonetti and A. Azzam, The h-p Clouds meshless method and lagrange multipliers for higher order elliptic operators . In preparation.