The p version of mixed finite element methods for parabolic problems

Sonia M. F. Garcia; Søren Jensen

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1997)

  • Volume: 31, Issue: 3, page 303-326
  • ISSN: 0764-583X

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Garcia, Sonia M. F., and Jensen, Søren. "The $p$ version of mixed finite element methods for parabolic problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 31.3 (1997): 303-326. <http://eudml.org/doc/193839>.

@article{Garcia1997,
author = {Garcia, Sonia M. F., Jensen, Søren},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = { version; error bounds; semidiscrete mixed finite element method; linear second order parabolic equation; stability; Raviart-Thomas projection},
language = {eng},
number = {3},
pages = {303-326},
publisher = {Dunod},
title = {The $p$ version of mixed finite element methods for parabolic problems},
url = {http://eudml.org/doc/193839},
volume = {31},
year = {1997},
}

TY - JOUR
AU - Garcia, Sonia M. F.
AU - Jensen, Søren
TI - The $p$ version of mixed finite element methods for parabolic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1997
PB - Dunod
VL - 31
IS - 3
SP - 303
EP - 326
LA - eng
KW - version; error bounds; semidiscrete mixed finite element method; linear second order parabolic equation; stability; Raviart-Thomas projection
UR - http://eudml.org/doc/193839
ER -

References

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  2. [2] F. BREZZI, 1974, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO 8-R.2, 129-151. Zbl0338.90047MR365287
  3. [3] M. R. DORR, 1984, The approximation theory for the p-version of the finite element method, SIAM J. Numer. Anal., 21, 1180-1207. Zbl0572.65074MR765514
  4. [4] J. Jr. DOUGLAS and J. E. ROBERTS, 1982, Mixed finite element methods for second order elliptic problems, Mat. Applic. Comp., 1, 91-103. Zbl0482.65057MR667620
  5. [5] J. Jr. DOUGLAS and J. E. ROBERTS, 1985, Global estimates for mixed methods for second order elliptic equations, Math. Comp., 44, 39-52. Zbl0624.65109MR771029
  6. [6] S. M. F. GARCIA, 1994, Improved Error Estimates for Nonlinear Parabolic Equations - Continuous Time Case, Numer. Methods in PDEs, 10, 129-147. Zbl0792.65068MR1259214
  7. [7] S. Jensen, 1992, p-version of the mixed finite element method for Stokes-like problems, Comp. Meth. Appl. Mech. Eng., 101, 27-41. Zbl0778.76052MR1195577
  8. [8] S. JENSEN and M. VOGELIUS, 1990, Divergence stability in connection with the p version of the finite element method, RAIRO, Modélisation Math. Anal. Numér., 24-6, 737-764. Zbl0717.65085MR1080717
  9. [9] C. JOHNSON, Numerical solutions of partial differential equations by the finite element methods, Cambridge University Press, 1987. MR925005
  10. [10] C. JOHNSON and V. THOMÉE, 1981, Error estimates for some mixed finite element methods for parabolic type problems, RAIRO Anal. Numér., 15, 41-78. Zbl0476.65074MR610597
  11. [11] F. A. MlLNER and M. SURI, 1992, Mixed Finite Element Methods for Quasilinear Second Order Elliptic Problems : the p-version. RAIRO, Modélisation Math. Anal. Numér., 24-7, 913-931. Zbl0783.65076MR1199319
  12. [12] A. QUARTERONI, 1984, Some results of Bernstein and Jackson type for polynomial approximation in Lp spaces, Jap. J. Appl. Math., 1, 173-181. Zbl0568.41006MR839312
  13. [13] P.-A. RAVIART and J. M. THOMAS, 1977, A Mixed Finite Element Method for 2-nd Order Elliptic Equations, in Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics, 606, ed. I. Galligani and E. Magenes, Springer, 292-315. Zbl0362.65089MR483555
  14. [14] G. SANSONE, Orthogonal Functions, Dover, Mineola, NY 1991 (orig. Interscience, 1959). Zbl0084.06106MR1118381
  15. [15] E. M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series vol. 30, Princeton University Press, NJ, 1970. Zbl0207.13501MR290095
  16. [16] M. SURI, 1990, On the stability and convergence of higher order mixed finite element methods for second order elliptic problems, Math. Comp., 54, 1-19. Zbl0687.65101MR990603
  17. [17] G. SZEGÖ, Orthogonal Polynomials, AMS Colloq. Publ. 23, 1933. Zbl0023.21505

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