Lagrange multipliers for higher order elliptic operators
ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 2, pp. 419-429.

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.

DOI : 10.1051/m2an:2005013
Classification : 41A10, 41A17, 65N15, 65N30
Mots-clés : elliptic operators, Dirichlet boundary-value problem, Lagrange multipliers 
@article{M2AN_2005__39_2_419_0,
     author = {Zuppa, Carlos},
     title = {Lagrange multipliers for higher order elliptic operators},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {419--429},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {2},
     year = {2005},
     doi = {10.1051/m2an:2005013},
     mrnumber = {2143954},
     zbl = {1078.65111},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/m2an:2005013/}
}
TY  - JOUR
AU  - Zuppa, Carlos
TI  - Lagrange multipliers for higher order elliptic operators
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2005
SP  - 419
EP  - 429
VL  - 39
IS  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/m2an:2005013/
DO  - 10.1051/m2an:2005013
LA  - en
ID  - M2AN_2005__39_2_419_0
ER  - 
%0 Journal Article
%A Zuppa, Carlos
%T Lagrange multipliers for higher order elliptic operators
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2005
%P 419-429
%V 39
%N 2
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/m2an:2005013/
%R 10.1051/m2an:2005013
%G en
%F M2AN_2005__39_2_419_0
Zuppa, Carlos. Lagrange multipliers for higher order elliptic operators. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 2, pp. 419-429. doi : 10.1051/m2an:2005013. http://archive.numdam.org/articles/10.1051/m2an:2005013/

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

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

[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

[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

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

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

[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

[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

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

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

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

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

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

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

Cité par Sources :