Superconvergence of mixed finite element methods for parabolic equations

Maria Cristina; J. Squeff

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1987)

  • Volume: 21, Issue: 2, page 327-352
  • ISSN: 0764-583X

How to cite

top

Cristina, Maria, and Squeff, J.. "Superconvergence of mixed finite element methods for parabolic equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.2 (1987): 327-352. <http://eudml.org/doc/193505>.

@article{Cristina1987,
author = {Cristina, Maria, Squeff, J.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {superconvergence; semidiscrete mixed finite element method; quasi- projection; asymptotic expansions; post-processing; Optimal order error estimates},
language = {eng},
number = {2},
pages = {327-352},
publisher = {Dunod},
title = {Superconvergence of mixed finite element methods for parabolic equations},
url = {http://eudml.org/doc/193505},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Cristina, Maria
AU - Squeff, J.
TI - Superconvergence of mixed finite element methods for parabolic equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 2
SP - 327
EP - 352
LA - eng
KW - superconvergence; semidiscrete mixed finite element method; quasi- projection; asymptotic expansions; post-processing; Optimal order error estimates
UR - http://eudml.org/doc/193505
ER -

References

top
  1. [1] D. N. ARNOLD and J. DOUGLAS Jr., Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable, Calcolo, 16 (1979), pp.345-369. Zbl0435.65094MR592476
  2. [2] J. H. BRAMBLE and A. H. SCHATZ, Estimates for spline projections, RAIRO Anal. Numér., 8 (1976), pp. 5-37. Zbl0343.65045MR436620
  3. [3] J. H BRAMBLE and A. H. SCHATZ, Higher order local accuracy by averaging in the finite element method, Math. Comp. 137 (1977), pp. 94-111. Zbl0353.65064MR431744
  4. [4] J. DOUGLAS Jr., Superconvergence in the pressure in the simulation of miscible displacement, SIAM J. Numer. Anal., 22 (1985), pp.962-969. Zbl0624.65124MR799123
  5. [5] J. DOUGLAS Jr., T. DUPONT and M. F. WHEELER, A quasi-projection analysis of Galerkin methods for parabolic and hyperbolic equations, Math. Comp., 142 (1978), pp. 345-362. Zbl0385.65052MR495012
  6. [6] J. DOUGLAS Jr., and F. A. MILNER, Interior and superconvergence estimates for mixed methods for second order elliptic problems, to Math. Modelling and Numer. Anal., 3 (1985), pp. 397-428. Zbl0613.65110MR807324
  7. [7] J. DOUGLAS Jr., and J. E. ROBERTS, Mixed finite element methods for second order elliptic problems, Mat. Apl. Comput., 1 (1982), pp.91-103. Zbl0482.65057MR667620
  8. [8] J. DOUGLAS Jr., and J. E. ROBERTS, Global estimates for mixed methods for second order elliptic equations, Math. Comp., 44 (1985), pp. 39-52. Zbl0624.65109MR771029
  9. [9] R. FALK and J. OSBORN, Error estimates for mixed methods, RAIRO Anal. Numér., 14 (1980), pp. 249-277. Zbl0467.65062MR592753
  10. [10] C. JOHNSON and V. THOMÉE, Error estimates for some mixed finite element methods for parabolic type problems, RAIRO Anal. Numér., 1 (1981), pp. 41-78. Zbl0476.65074MR610597
  11. [11] J. C. NEDELEC, Mixed finite elements in R3, Numer. Math., 35 (1980), pp. 315-341. Zbl0419.65069MR592160
  12. [12] P. A. RAVI ART and J. M. THOMAS, A mixed finite element method for second order elliptic problems, in Proceedings of a conference on Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics 606, Springer-Verlag, Berlin, 1977, p. 292-315. Zbl0362.65089MR483555
  13. [13] M. C. SQUEFF, Superconvergence of Mixed Finite Element Methods for Parabolic Equation, Thesis, The University of Chicago, August 1985. 
  14. [14] J. M. THOMAS, Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes, Thèse, Université P. et M. Curie, Paris, 1977. 
  15. [15] V. THOMÉE, Negative norm estimates and superconvergence in Galerkin methods for parabolic problems, Math. Comp., 34 (1980), pp.93-113. Zbl0454.65077MR551292

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.