×

zbMATH — the first resource for mathematics

Lagrange multipliers for higher order elliptic operators. (English) Zbl 1078.65111
The author presents an extended analysis of Babuska’s theory of Lagrange multipliers for higher order elliptic Dirichlet problems. A numerical implementation of the methodology is formulated and a set of numerical results is shown as illustration.
MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
Software:
Mfree2D
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] S. Agmon , Lectures on elliptic boundary value problems . D. Van Nostrand, Princeton, N. J. ( 1965 ). MR 178246 | Zbl 0142.37401 · Zbl 0142.37401
[2] I. Babuška , The finite element method with lagrange multipliers . Numer. Math. 20 ( 1973 ) 179 - 192 . Article | Zbl 0258.65108 · 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 · 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 · 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 · 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 · 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 · 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 · Zbl 1031.74001
[11] J. Nečas , Les méthodes directes en théorie des équations elliptiques . Masson, Paris ( 1967 ). MR 227584 · Zbl 1225.35003
[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 · Zbl 0336.35001
[13] K.T. Smith , Inequalities for formally positive integro-differential forms . Bull. Amer. Math. Soc. 67 ( 1961 ) 368 - 370 . Article | Zbl 0103.07602 · 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 · 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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.