Error estimates for some mixed finite element methods for parabolic type problems

Claes Johnson; Vidar Thomee

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1981)

  • Volume: 15, Issue: 1, page 41-78
  • ISSN: 0764-583X

How to cite

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Johnson, Claes, and Thomee, Vidar. "Error estimates for some mixed finite element methods for parabolic type problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 15.1 (1981): 41-78. <http://eudml.org/doc/193370>.

@article{Johnson1981,
author = {Johnson, Claes, Thomee, Vidar},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mixed finite element methods; Stokes' equations},
language = {eng},
number = {1},
pages = {41-78},
publisher = {Dunod},
title = {Error estimates for some mixed finite element methods for parabolic type problems},
url = {http://eudml.org/doc/193370},
volume = {15},
year = {1981},
}

TY - JOUR
AU - Johnson, Claes
AU - Thomee, Vidar
TI - Error estimates for some mixed finite element methods for parabolic type problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1981
PB - Dunod
VL - 15
IS - 1
SP - 41
EP - 78
LA - eng
KW - mixed finite element methods; Stokes' equations
UR - http://eudml.org/doc/193370
ER -

References

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  1. 1. S. AGMON, A. DOUGLIS and L. NIRENBERG, Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions, Comm. Pure AppL Math., Vol. 12, 1959, pp. 623-727. Zbl0093.10401MR125307
  2. 2. G. A. BAKER, J. H. BRAMBLE and V. THOMÉE, Single Step Galerkin Approximations for Parabolic Problems, Math. Comp., Vol.31, 1977 pp. 818-847. Zbl0378.65061MR448947
  3. 3. J. H. BRAMBLE and J. OSBORN, Rate of Convergence Estimates for Non-Selfadjoint Eigenvalue Approximations, Math. Comp., Vol. 27, 1973, pp. 525-549. Zbl0305.65064MR366029
  4. 4. J. H. BRAMBLE, A. H. SCHATZ, V. THOMÉE and L. B. WAHLBIN, Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations, S.I.A.M. J. Numer. Anal., Vol. 14, 1977, pp. 218-241. Zbl0364.65084MR448926
  5. 5. J. H. BRAMBLE and V. THOMÉE, Discrete Time Galerkin Methods for a Parabolic Boundary Value Problem, Annali di Matematica pura ed applicata, Vol. 101, 1974 pp. 115-152. Zbl0306.65073MR388805
  6. 6. F. BREZZI, On the Existence, Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrangian Multipliers, R.A.I.R.O., Anal. Numér., Vol.2, 1974, pp. 129-151. Zbl0338.90047MR365287
  7. 7. A. CALDERON and A. ZYGMUND, On theExistence of Certain Singuiar Integrals, Acta Math., Vol.88, 1952, pp. 85-139. Zbl0047.10201MR52553
  8. 8. G. DUVAUT and J. L. LIONS, Les inéquations en mécanique et enphysique, Dunod, Paris, 1972. Zbl0298.73001MR464857
  9. 9. R. FALK and J. OSBORN, Error Estimates for Mixed Methods, Technical report, The Mathematics Research Center, University of Wisconsin-Madison, 1979. Zbl0467.65062MR592753
  10. 10. C. JENSEN, A Mixed Finite Element Method with Curved Eléments, Technical report, Department of Computer Science, Chalmers University of Technology, 1979. 
  11. 11. C. JOHNSON, A Mixed Finite Element Method for Navier-Stokes' Equatiom, R.A I. R.O., Anal. Numér., Vol. 12, 1978, pp. 335-348. Zbl0399.76035MR519017
  12. 12. C. JOHNSON and B. MERCIER, Some Equilibrium Finite Element Methods for Two-Dimensional Elasticity Problems, Numer. Math., Vol. 30, 1978, pp. 103-116. Zbl0427.73072MR483904
  13. 13. P. A. RAVIART and J. M. THOMAS, A Mixed Finite Element Method for 2nd Order Elliptic Problems, Proc. of the Symposium on the Mathematîcal Aspects of the Finite Element Method, Rome, December, 1975. Zbl0362.65089
  14. 14. R. SCHOLZ, L -Convergence of Saddle-Point Approximation for Second Order Problems,R.A.I.R.O., Anal. Numér., Zbl0356.35026
  15. 15. R. TEMAM, Navier-Stokes' Equations, North Holland. Amsterdam, 1977. Zbl0383.35057
  16. 16. J. M. THOMAS, Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes, Thèse, Université Pierre-et-Marie-Curie, Paris, 1977. 
  17. 17. V. THOMÉE, Some Interior Estimates for Semidiscrete Galerkin Approximations for Parabolic Equations, Math. Comp., Vol.33, 1979, pp. 37-62. Zbl0419.65073MR514809

Citations in EuDML Documents

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  1. Jérôme Jaffre, Jean E. Roberts, Upstream weighting and mixed finite elements in the simulation of miscible displacements
  2. Jim Jr. Douglas, Richard E. Ewing, Mary Fanett Wheeler, A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media
  3. Sonia M. F. Garcia, Søren Jensen, The p version of mixed finite element methods for parabolic problems
  4. Maria Cristina, J. Squeff, Superconvergence of mixed finite element methods for parabolic equations
  5. Yuting Wei, Stabilized finite element methods for miscible displacement in porous media
  6. Tunc Geveci, On the application of mixed finite element methods to the wave equations
  7. Ricardo G. Durán, Error analysis in L p p , for mixed finite element methods for linear and quasi-linear elliptic problems
  8. Lucia Gastaldi, Ricardo H. Nochetto, Sharp maximum norm error estimates for general mixed finite element approximations to second order elliptic equations

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