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.
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://www.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://www.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://www.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://www.numdam.org/articles/10.1051/m2an:2005013/
[1] Lectures on elliptic boundary value problems. D. Van Nostrand, Princeton, N. J. (1965). | MR | Zbl
,[2] The finite element method with lagrange multipliers. Numer. Math. 20 (1973) 179-192. | Zbl
,[3] 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
and ,[4] 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] Expansions in Eigenfunctions of Self-Adjoint Operators, Translations of Mathematical Monographs 17, American Mathematical Society, Providence, R.I. (1968). | MR
,[6] The mathematical theory of finite elements methods. Springer-Verlag, New York (1994). | MR | Zbl
and ,[7] H-p clouds - an h-p meshless method. Num. Methods Partial Differential Equations. 1 (1996) 1-34. | Zbl
and ,[8] Meshfree and particle methods and their applications. Applied Mechanics Reviews (ASME) (2001).
and ,[9] Problèmes aux limites non homogènes et applications. Dunod, Paris (1968). | Zbl
and ,[10] Mesh Free Methods: Moving Beyond the Finite Element Method. CRC Press, Boca Raton, USA (2002). | MR | Zbl
,[11] Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967). | MR
,[12] An introduction to the mathematical theory of finite elements. Wiley Interscience, New York (1976). | MR | Zbl
and ,[13] Inequalities for formally positive integro-differential forms. Bull. Amer. Math. Soc. 67 (1961) 368-370. | Zbl
,[14] Solvability of boundary value problems for general elliptic systems. Amer. Math. Soc. Transl. 67 (1968) 182-225. | Zbl
,[15] The h-p Clouds meshless method and lagrange multipliers for higher order elliptic operators. In preparation.
, and ,Cité par Sources :