The p version of mixed finite element methods for parabolic problems
Garcia, Sonia M. F. ; Jensen, Søren
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 31 (1997), p. 303-326 / Harvested from Numdam
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Publié le : 1997-01-01
@article{M2AN_1997__31_3_303_0,
     author = {Garcia, Sonia M. F. and Jensen, S\o ren},
     title = {The $p$ version of mixed finite element methods for parabolic problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {31},
     year = {1997},
     pages = {303-326},
     mrnumber = {1451345},
     zbl = {0876.65070},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1997__31_3_303_0}
}

Garcia, Sonia M. F.; Jensen, Søren. The $p$ version of mixed finite element methods for parabolic problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 31 (1997) pp. 303-326. http://gdmltest.u-ga.fr/item/M2AN_1997__31_3_303_0/

[1] I. Babuška, 1971, Error bounds for the finite element method, Numer. Math., 16,322-333. | MR 288971 | Zbl 0214.42001

[2] F. Brezzi, 1974, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO 8-R.2, 129-151. | Numdam | MR 365287 | Zbl 0338.90047

[3] M. R. Dorr, 1984, The approximation theory for the p-version of the finite element method, SIAM J. Numer. Anal., 21, 1180-1207. | MR 765514 | Zbl 0572.65074

[4] J. Jr. Douglas and J. E. Roberts, 1982, Mixed finite element methods for second order elliptic problems, Mat. Applic. Comp., 1, 91-103. | MR 667620 | Zbl 0482.65057

[5] J. Jr. Douglas and J. E. Roberts, 1985, Global estimates for mixed methods for second order elliptic equations, Math. Comp., 44, 39-52. | MR 771029 | Zbl 0624.65109

[6] S. M. F. Garcia, 1994, Improved Error Estimates for Nonlinear Parabolic Equations - Continuous Time Case, Numer. Methods in PDEs, 10, 129-147. | MR 1259214 | Zbl 0792.65068

[7] S. Jensen, 1992, p-version of the mixed finite element method for Stokes-like problems, Comp. Meth. Appl. Mech. Eng., 101, 27-41. | MR 1195577 | Zbl 0778.76052

[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. | Numdam | MR 1080717 | Zbl 0717.65085

[9] C. Johnson, Numerical solutions of partial differential equations by the finite element methods, Cambridge University Press, 1987. | MR 925005

[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. | Numdam | MR 610597 | Zbl 0476.65074

[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. | Numdam | MR 1199319 | Zbl 0783.65076

[12] A. Quarteroni, 1984, Some results of Bernstein and Jackson type for polynomial approximation in Lp spaces, Jap. J. Appl. Math., 1, 173-181. | MR 839312 | Zbl 0568.41006

[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. | MR 483555 | Zbl 0362.65089

[14] G. Sansone, Orthogonal Functions, Dover, Mineola, NY 1991 (orig. Interscience, 1959). | MR 1118381 | Zbl 0084.06106

[15] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series vol. 30, Princeton University Press, NJ, 1970. | MR 290095 | Zbl 0207.13501

[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. | MR 990603 | Zbl 0687.65101

[17] G. Szegö, Orthogonal Polynomials, AMS Colloq. Publ. 23, 1933. | Zbl 0023.21505