Lagrange multipliers for higher order elliptic operators

Carlos Zuppa

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

  • Volume: 39, Issue: 2, page 419-429
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Zuppa, Carlos. "Lagrange multipliers for higher order elliptic operators." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.2 (2005): 419-429. <http://eudml.org/doc/244797>.

@article{Zuppa2005,
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.},
author = {Zuppa, Carlos},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {elliptic operators; Dirichlet boundary-value problem; Lagrange multipliers; Dirichlet boundary value problem; finite element method; numerical results},
language = {eng},
number = {2},
pages = {419-429},
publisher = {EDP-Sciences},
title = {Lagrange multipliers for higher order elliptic operators},
url = {http://eudml.org/doc/244797},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Zuppa, Carlos
TI - Lagrange multipliers for higher order elliptic operators
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 2
SP - 419
EP - 429
AB - 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.
LA - eng
KW - elliptic operators; Dirichlet boundary-value problem; Lagrange multipliers; Dirichlet boundary value problem; finite element method; numerical results
UR - http://eudml.org/doc/244797
ER -

References

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  1. [1] S. Agmon, Lectures on elliptic boundary value problems. D. Van Nostrand, Princeton, N. J. (1965). Zbl0142.37401MR178246
  2. [2] I. Babuška, The finite element method with lagrange multipliers. Numer. Math. 20 (1973) 179–192. Zbl0258.65108
  3. [3] 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. Zbl0268.65052
  4. [4] T. Belytschko, Y. Krongauz. D. Organ, M. Fleming and P. Krysl, Meshless methods: an overview and recent development. Comput. Methods Appl. Mech. Engrg. 139 (1996a) 3–47. Zbl0891.73075
  5. [5] J.M. Berezanskii, Expansions in Eigenfunctions of Self-Adjoint Operators, Translations of Mathematical Monographs 17, American Mathematical Society, Providence, R.I. (1968). MR222718
  6. [6] S.C. Brener and L.R. Scott, The mathematical theory of finite elements methods. Springer-Verlag, New York (1994). Zbl0804.65101MR1278258
  7. [7] C.A. Duarte and J.T. Oden, H-p clouds - an h-p meshless method. Num. Methods Partial Differential Equations. 1 (1996) 1–34. Zbl0869.65069
  8. [8] S. Li and W.K. Liu, Meshfree and particle methods and their applications. Applied Mechanics Reviews (ASME) (2001). 
  9. [9] J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Dunod, Paris (1968). Zbl0165.10801
  10. [10] G.R. Liu, Mesh Free Methods: Moving Beyond the Finite Element Method. CRC Press, Boca Raton, USA (2002). Zbl1031.74001MR1989981
  11. [11] J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967). MR227584
  12. [12] J.T. Oden and J.N. Reddy, An introduction to the mathematical theory of finite elements. Wiley Interscience, New York (1976). Zbl0336.35001MR461950
  13. [13] K.T. Smith, Inequalities for formally positive integro-differential forms. Bull. Amer. Math. Soc. 67 (1961) 368–370. Zbl0103.07602
  14. [14] L.R. Volevič, Solvability of boundary value problems for general elliptic systems. Amer. Math. Soc. Transl. 67 (1968) 182–225. Zbl0177.37401
  15. [15] C. Zuppa, G. Simonetti and A. Azzam, The h-p Clouds meshless method and lagrange multipliers for higher order elliptic operators. In preparation. 

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