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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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. Christine Bernardi, Adel Blouza, Nejmeddine Chorfi, Nizar Kharrat, A penalty algorithm for the spectral element discretization of the Stokes problem
  3. Eric Boillat, Finite element methods on non-conforming grids by penalizing the matching constraint
  4. Eric Boillat, Finite element methods on non-conforming grids by penalizing the matching constraint
  5. Christine Bernardi, Adel Blouza, Nejmeddine Chorfi, Nizar Kharrat, A penalty algorithm for the spectral element discretization of the Stokes problem
  6. Tunc Geveci, B. Daya Reddy, Howard T. Pearce, On the approximation of the spectrum of the Stokes operator

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