Two mixed finite element methods for the simply supported plate problem

James H. Bramble; Richard S. Falk

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1983)

  • Volume: 17, Issue: 4, page 337-384
  • ISSN: 0764-583X

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Bramble, James H., and Falk, Richard S.. "Two mixed finite element methods for the simply supported plate problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 17.4 (1983): 337-384. <http://eudml.org/doc/193421>.

@article{Bramble1983,
author = {Bramble, James H., Falk, Richard S.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {biharmonic model; simply supported plate; mixed formulation; lower order polynomials; two approximate schemes; error estimates; efficient computational procedures},
language = {eng},
number = {4},
pages = {337-384},
publisher = {Dunod},
title = {Two mixed finite element methods for the simply supported plate problem},
url = {http://eudml.org/doc/193421},
volume = {17},
year = {1983},
}

TY - JOUR
AU - Bramble, James H.
AU - Falk, Richard S.
TI - Two mixed finite element methods for the simply supported plate problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1983
PB - Dunod
VL - 17
IS - 4
SP - 337
EP - 384
LA - eng
KW - biharmonic model; simply supported plate; mixed formulation; lower order polynomials; two approximate schemes; error estimates; efficient computational procedures
UR - http://eudml.org/doc/193421
ER -

References

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  1. [1] O. AXELSSON, Solution of linear systems of equations : iterative methods, Sparse Matrix Techniques, V. A. Barker (editor), Lecture Notes in Mathematics 572, Springer-Verlag, 1971. Zbl0354.65021MR448834
  2. [2] 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 Applications to Partial Differential Equations, A. K. Aziz (Editor), Academic Press, New York, 1972. Zbl0268.65052MR421106
  3. [3] I. BABUŠKA, The finite element method with Lagrangian multipliers, Numer. Math. 20 (1973), pp. 179-192. Zbl0258.65108MR359352
  4. [4] J. H. BRAMBLE and J. E. OSBORN, Rate of convergence estimates for nonselfadjoint eigenvalue approximations, Math. Comp. 27 (1973), pp. 525-549. Zbl0305.65064MR366029
  5. [5] J. H. BRAMBLE and L. E. PAYNE, Some Uniqueness Theorems in the Theory of Elasticity, Arch. for Rat. Mech. and Anal., 9 (1962), pp. 319-328. Zbl0103.40402MR143374
  6. [6] J. H. BRAMBLE and L. R. SCOTT, Simultaneous approximation in scales of Banach spaces, Math. Comp. 32 (1978), pp. 947-954. Zbl0404.41005MR501990
  7. [7] J. H. BRAMBLE, The lagrange multiplier method for Dirichlet's problem, Math. Comp. 37 (1981), pp. 1-11. Zbl0477.65077MR616356
  8. [8] 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. Zbl0337.65058MR657977
  9. [9] P. G. CIARLET and R. GLOWINSKI, Dual iterative techniques for solving a finite element approximation of the biharmonic equation, Comput. Methods Appl. Mech. Engrg., 5 (1975), pp. 277-295. Zbl0305.65068MR373321
  10. [10] R. S. FALK, Approximation of the biharmonic equation by a mixed finite element method, SIAM J. Numer. Anal., 15 (1978), pp. 556-567. Zbl0383.65059MR478665
  11. [11] 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. Zbl0427.65073MR524511
  12. [12] J. L. LIONS and E. MAGENES, Problèmes aux limites non homogènes et applications, vol. 1, Dunod, Paris, 1968. Zbl0165.10801MR247243
  13. [13] M. SCHECHTER, On On L p estimates and regularity II, Math. Scand. 13 (1963), pp. 47-69. Zbl0131.09505MR188616
  14. [14] R. WEINSTOCK, Calculus of Variations, McGraw-Hill, New York, 1952. Zbl0049.19503

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