Lagrange multipliers for higher order elliptic operators
Zuppa, Carlos
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005), p. 419-429 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

Publié le : 2005-01-01
DOI : https://doi.org/10.1051/m2an:2005013
Classification:  41A10,  41A17,  65N15,  65N30 
@article{M2AN_2005__39_2_419_0,
     author = {Zuppa, Carlos},
     title = {Lagrange multipliers for higher order elliptic operators},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {39},
     year = {2005},
     pages = {419-429},
     doi = {10.1051/m2an:2005013},
     mrnumber = {2143954},
     zbl = {1078.65111},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2005__39_2_419_0}
}

Zuppa, Carlos. Lagrange multipliers for higher order elliptic operators. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 419-429. doi : 10.1051/m2an:2005013. http://gdmltest.u-ga.fr/item/M2AN_2005__39_2_419_0/

[1] S. Agmon, Lectures on elliptic boundary value problems. D. Van Nostrand, Princeton, N. J. (1965). | MR 178246 | Zbl 0142.37401

[2] I. Babuška, The finite element method with lagrange multipliers. Numer. Math. 20 (1973) 179-192. | Zbl 0258.65108

[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. | Zbl 0268.65052

[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. | Zbl 0891.73075

[5] J.M. Berezanskii, Expansions in Eigenfunctions of Self-Adjoint Operators, Translations of Mathematical Monographs 17, American Mathematical Society, Providence, R.I. (1968). | MR 222718

[6] S.C. Brener and L.R. Scott, The mathematical theory of finite elements methods. Springer-Verlag, New York (1994). | MR 1278258 | Zbl 0804.65101

[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. | Zbl 0869.65069

[8] S. Li and W.K. Liu, Meshfree and particle methods and their applications. Applied Mechanics Reviews (ASME) (2001).

[9] J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Dunod, Paris (1968). | Zbl 0165.10801

[10] G.R. Liu, Mesh Free Methods: Moving Beyond the Finite Element Method. CRC Press, Boca Raton, USA (2002). | MR 1989981 | Zbl 1031.74001

[11] J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967). | MR 227584

[12] J.T. Oden and J.N. Reddy, An introduction to the mathematical theory of finite elements. Wiley Interscience, New York (1976). | MR 461950 | Zbl 0336.35001

[13] K.T. Smith, Inequalities for formally positive integro-differential forms. Bull. Amer. Math. Soc. 67 (1961) 368-370. | Zbl 0103.07602

[14] L.R. Volevič, Solvability of boundary value problems for general elliptic systems. Amer. Math. Soc. Transl. 67 (1968) 182-225. | Zbl 0177.37401

[15] C. Zuppa, G. Simonetti and A. Azzam, The h-p Clouds meshless method and lagrange multipliers for higher order elliptic operators. In preparation.