A mixed-Lagrange multiplier finite element method for the polyharmonic equation

James H. Bramble; Richard S. Falk

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1985)

  • Volume: 19, Issue: 4, page 519-557
  • ISSN: 0764-583X

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Bramble, James H., and 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 19.4 (1985): 519-557. <http://eudml.org/doc/193458>.

@article{Bramble1985,
author = {Bramble, James H., Falk, Richard S.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mixed methods; error estimates; polyharmonic equation; conforming finite element method; Galerkin method; conjugate gradient method; Lagrange multipliers},
language = {eng},
number = {4},
pages = {519-557},
publisher = {Dunod},
title = {A mixed-Lagrange multiplier finite element method for the polyharmonic equation},
url = {http://eudml.org/doc/193458},
volume = {19},
year = {1985},
}

TY - JOUR
AU - Bramble, James H.
AU - Falk, Richard S.
TI - A mixed-Lagrange multiplier finite element method for the polyharmonic equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1985
PB - Dunod
VL - 19
IS - 4
SP - 519
EP - 557
LA - eng
KW - mixed methods; error estimates; polyharmonic equation; conforming finite element method; Galerkin method; conjugate gradient method; Lagrange multipliers
UR - http://eudml.org/doc/193458
ER -

References

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  1. [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. Zbl0354.65021MR448834
  2. [2] I. BABUSKA, The finite element method with Lagrangian multipliers, Numer. Math., 20 (1973), pp. 179-192. Zbl0258.65108MR359352
  3. [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. Zbl0268.65052MR421106
  4. [4] J. H. BRAMBLE, The Lagrange multiplier method for Dirichlet's Problem, Math.Comp., 37 (1981), pp. 1-11 Zbl0477.65077MR616356
  5. [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. Zbl0536.73063MR713765
  6. [6] J . H . BRAMBLE and J. E. OSBORN, Rate of convergence estimates for non-selfadjoint eigenvalue approximations. Math. Comp.. 27 (1973). pp. 525-549 Zbl0305.65064MR366029
  7. [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. [8] J. H. BRAMBLE and L. R. SCOTT, Simultaneous approximation in scales of Banach spaces, Math. Comp., 32 (1978), pp.947-954. Zbl0404.41005MR501990
  9. [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. Zbl0337.65058MR657977
  10. [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. Zbl0305.65068MR373321
  11. [11] 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
  12. [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. Zbl0427.65073MR524511
  13. [13] J. L. LIONS and E. MAGENES, Problèmes Aux Limites non Homogènes et Applications, Vol 1, Dunod, Paris, 1968. Zbl0165.10801MR247243
  14. [14] M. SCHECHTER, On L p estimates andregularity II, Math. Scand., 13 (1963), pp. 47- Zbl0131.09505MR188616

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