A mixed-Lagrange multiplier finite element method for the polyharmonic equation
Bramble, James H. ; Falk, Richard S.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 19 (1985), p. 519-557 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1985-01-01
@article{M2AN_1985__19_4_519_0,
     author = {Bramble, James H. and Falk, Richard S.},
     title = {A mixed-Lagrange multiplier finite element method for the polyharmonic equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {19},
     year = {1985},
     pages = {519-557},
     mrnumber = {826223},
     zbl = {0591.65073},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1985__19_4_519_0}
}

Bramble, James H.; Falk, Richard S. A mixed-Lagrange multiplier finite element method for the polyharmonic equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 19 (1985) pp. 519-557. http://gdmltest.u-ga.fr/item/M2AN_1985__19_4_519_0/

[1] O. Axelsson, Solution of linear Systems of équations : itérative methods. Sparse Matrix Techniques, V. A. Barker (editor), Lecture Notes in Mathematics 572, Springer Verlag, 1977. | MR 448834 | Zbl 0354.65021

[2] I. Babuska, The finite element method with Lagrangian multipliers, Numer. Math., 20 (1973), pp. 179-192. | MR 359352 | Zbl 0258.65108

[3] I. Babuska and A. K. Aziz, Survey lectures on the mathematical foundations of the finite element method, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A. K. Aziz (editor), Academic Press, New York, 1972. | MR 421106 | Zbl 0268.65052

[4] J. H. Bramble, The Lagrange multiplier method for Dirichlet's Problem, Math.Comp., 37 (1981), pp. 1-11 | MR 616356 | Zbl 0477.65077

[5] J. H. Bramble and R. S. Falk, TWO mixed finite element methods for the simply supported plate problem, R.A.I.R.O., Analyse numérique, 17 (1983), pp. 337-384. | Numdam | MR 713765 | Zbl 0536.73063

[6] J . H . Bramble and J. E. Osborn, Rate of convergence estimates for non-selfadjoint eigenvalue approximations. Math. Comp.. 27 (1973). pp. 525-549 | MR 366029 | Zbl 0305.65064

[7] J. H. Bramble and J. E. Pasciak, A new computational approach for the linearized scalar potential formulation of the magnetostatic field problem, EEE Transactions on Magnetics, Vol Mag-18, (1982), pp. 357-361.

[8] J. H. Bramble and L. R. Scott, Simultaneous approximation in scales of Banach spaces, Math. Comp., 32 (1978), pp.947-954. | MR 501990 | Zbl 0404.41005

[9] P. G. Ciarlet and P.A. Raviart, A mixed finite element method for the biharmonic equation, Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations, C. DeBoor, Ed., Academic Press, New York, 1974, pp. 125-143. | MR 657977 | Zbl 0337.65058

[10] P. G. Ciarlet and R. Glowinski, Dual itérative techniques for solving a finite element approximation of the biharmonic equation, Comput. Methods Appl. Mech. Engrg., 5 (1975), pp.277-295. | MR 373321 | Zbl 0305.65068

[11] R. S., Falk, Approximation of the biharmonic equation by a mixed finite element method, SIAM J. Numer. Anal., 15 (1978), pp.556-567. | MR 478665 | Zbl 0383.65059

[12] R. Glowinski and O. Pironneau, Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem, SIAM Review, 21 (1979), pp. 167-212. | MR 524511 | Zbl 0427.65073

[13] J. L. Lions and E. Magenes, Problèmes Aux Limites non Homogènes et Applications, Vol 1, Dunod, Paris, 1968. | MR 247243 | Zbl 0165.10801

[14] M. Schechter, On L p estimates andregularity II, Math. Scand., 13 (1963), pp. 47- | MR 188616 | Zbl 0131.09505