Perturbation of mixed variational problems. Application to mixed finite element methods

M. Bercovier

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1978)

  • Volume: 12, Issue: 3, page 211-236
  • ISSN: 0764-583X

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Bercovier, M.. "Perturbation of mixed variational problems. Application to mixed finite element methods." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 12.3 (1978): 211-236. <http://eudml.org/doc/193320>.

@article{Bercovier1978,
author = {Bercovier, M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mixed finite element formulation; mixed variational problem; Lagrange multiplier; stiffness matrix; small regular perturbation; penalty function},
language = {eng},
number = {3},
pages = {211-236},
publisher = {Dunod},
title = {Perturbation of mixed variational problems. Application to mixed finite element methods},
url = {http://eudml.org/doc/193320},
volume = {12},
year = {1978},
}

TY - JOUR
AU - Bercovier, M.
TI - Perturbation of mixed variational problems. Application to mixed finite element methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1978
PB - Dunod
VL - 12
IS - 3
SP - 211
EP - 236
LA - eng
KW - mixed finite element formulation; mixed variational problem; Lagrange multiplier; stiffness matrix; small regular perturbation; penalty function
UR - http://eudml.org/doc/193320
ER -

References

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  1. 1 J P AUBIN, Approximation of Elliptic Boundary Value Problems, Wiley, N Y , 1972 Zbl0248.65063MR478662
  2. 2 I BABUSKA, The Finite Element Method with Lagraman Multipliers, Num Math ,Vol 20, 1973, pp 179-192 Zbl0258.65108MR359352
  3. 3 I BABUSKA, The Finite Element Method with Penalty, Math Comp , Vol 27, 1973, pp 221-228 Zbl0299.65057MR351118
  4. 4 M BERCOVIER, A Family of Fini te Eléments with Penahzation for the NumencalSolution ofStokes and Navier-Stokes Equations, m Proc I F I P Conf 1977,North-Holland, Amsterdam, 1977 Zbl0383.65065MR483540
  5. 5 M BERCOVIER, On the Penalty and Extrapolation Method (to appear) Zbl0486.73070
  6. 5 bis. M BERCOVIER, Thèse de Doctorat d'État, Rouen, 1976 
  7. 6 M BERCOVIER, and M ENGELMANA Finite Element for the Numencal Solution ofViscous Incompressible flous (to appear m J Comp Phys ) Zbl0395.76040
  8. 7 M BERCOVIER and F LIVNFA 4 CSTQuadïilateial Element for Incompressible andNecul Incompressible Mateuals (to appear in CALCOLO) Zbl0418.73009
  9. 8 F BREZZIOn the Existence, Uniqueness and Approximation of saddle Point ProblemsAnsing jiom Lagrangian Multipliers, R A I R O Vol 8 R-2 1974 pp 129-151 Zbl0338.90047MR365287
  10. 9 F BREZZI and P A RAVIART, Mixed Finite Element Methods jor Ath OrderElhptic Equations, Topics m Numencal Analysis, Vol III, J J H MILLER Ed , Academic Press 
  11. 10 P G CIARLET, Numencal Analysis oj the Finite Element Method for Elliptic BoundaryValue Problems, North Holland, Amsterdam, 1977 MR1115235
  12. 11 A J CHORIN, A Numencal Method for Solving Incompressible Problems, J CompPhys , Vol 2, 1967 Zbl0149.44802
  13. 12 M CROUZEIX and P A RAVIART, Conforming and non Conforming Finite ElémentsMethods for Solving the Statwnary Stokes Equation R A I R O, Vol 7, R-3, 1973, pp 33-76 Zbl0302.65087MR343661
  14. 13 G DUVAUT and J L LIONS, Les inéquations en mécanique et en physique, Dunod,Pans, 1972 Zbl0298.73001MR464857
  15. 14 I EKELAND and R TEMAM, Analyse convexe et problèmes vanationnels , Dunod, Pans, 1974 Zbl0281.49001
  16. 15 M FORTIN, Thèse de Doctorat d'État, Pans, 1972 
  17. 15 bis. M FORTIN, An Analysis of the Convergence of Mixed Finite Element Methods, R A I R O , Vol 11, R-3, 1977, pp 341-354 Zbl0373.65055MR464543
  18. 16 L R HERRMANNElastuttx Equations for Incompressible or Nearly IncompressibleMaterials by a Vanational Theorem A I A A Journal, Vol 3, 1965, pp 1896-1900 MR184477
  19. 17 P A RAVIART and J M THOMAS, A Mixed Finite Element Method for 2nd OrderElliptic Problems, in Proc Symp on the Mathematical aspects oj the FEM Rome,December 1975, Lecture notes m Mathematics 606, Springer Verlag, pp 292-315 Zbl0362.65089MR483555
  20. 18 R TEMAM, Une méthode d'approximation de la solution des équations de Navier-Stokes, Bull Soc Math Fr , Vol 96, 1968 Zbl0181.18903MR237972
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  22. 20 J M THOMAS, Thèse de Doctorat d'État, Pans, 1977 

Citations in EuDML Documents

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  1. C. Atamian, P. Joly, Une analyse de la méthode des domaines fictifs pour le problème de Helmholtz extérieur
  2. Eric Boillat, Finite element methods on non-conforming grids by penalizing the matching constraint
  3. Christine Bernardi, Adel Blouza, Nejmeddine Chorfi, Nizar Kharrat, A penalty algorithm for the spectral element discretization of the Stokes problem
  4. Tunc Geveci, B. Daya Reddy, Howard T. Pearce, On the approximation of the spectrum of the Stokes operator
  5. Christine Bernardi, Adel Blouza, Nejmeddine Chorfi, Nizar Kharrat, A penalty algorithm for the spectral element discretization of the Stokes problem
  6. Eric Boillat, Finite element methods on non-conforming grids by penalizing the matching constraint

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