Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities
ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 6, pp. 725-744. 
@article{M2AN_1994__28_6_725_0,
     author = {Liu, W. B. and Barrett, John W.},
     title = {Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {725--744},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {28},
     number = {6},
     year = {1994},
     mrnumber = {1302421},
     zbl = {0820.65073},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_6_725_0/}
}
TY  - JOUR
AU  - Liu, W. B.
AU  - Barrett, John W.
TI  - Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1994
SP  - 725
EP  - 744
VL  - 28
IS  - 6
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1994__28_6_725_0/
LA  - en
ID  - M2AN_1994__28_6_725_0
ER  - 
%0 Journal Article
%A Liu, W. B.
%A Barrett, John W.
%T Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1994
%P 725-744
%V 28
%N 6
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1994__28_6_725_0/
%G en
%F M2AN_1994__28_6_725_0
Liu, W. B.; Barrett, John W. Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities. ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 6, pp. 725-744. http://www.numdam.org/item/M2AN_1994__28_6_725_0/

[1] C. Atkinson, C. R. Champion, 1984, Some boundary-value problems for the equation ∇ (|∇φ|N ∇φ) = 0. Q. Jl Mech. Appl. Math., 37, 401-419. | MR | Zbl

[2] J. W. Barrett, W. B. Liu, 1993, Finite element approximation of the p-Laplacian, Math. Comp., 61. 523-537. | MR | Zbl

[3] J. W. Barrett, W. B. Liu, 1993, Finite element error analysis of a quasi-Newtoman flow obeying the Carreau or power law, Numer. Math., 64, 433-453. | MR | Zbl

[4] L. W. Barrett, W. B. Liu, 1994, Finite element approximation of the parabolic p-Laplacian, SIAM, J. Numer. Anal., 31, 413-428. | MR | Zbl

[5] H. J. Choe, 1991, A regularity theory for a general class of quasilmear elliptic partial differential equations and obstacle problems, Arch. Rat. Mech. Anal., 114, 383-394. | MR | Zbl

[6] S. S. Chow, 1989, Finite element error estimates for non-linear elliptic equations of monotone type, Numer. Math. 54, 373-393. | MR | Zbl

[7] P.-G. Ciarlet, 1978, The Finite Element Methodfor Elliptic Problems, North. Holland, Amsterdam. | MR | Zbl

[8] P. Cortey-Dumont, 1985, On finite element approximation in the L∞-norm of variational inequalities, Numer. Math., 47, 45-57. | MR | Zbl

[9] M. Dobrowolski, R. Rannacher, 1980, Finite element methods for nonlinear elliptic Systems of second order, Math. Nachr., 94, 155-172. | MR | Zbl

[10] R. S. Falk, 1974, Error estimates for the approximation of a class of variational inequalities, Math. Comp., 28, 963-971. | MR | Zbl

[11] J. Frehse, R. Rannacher, 1978, Asymptotic L∞-error estimates for linear finite element approximations of quasilinear boundary problems, SIAM, J. Numer. Anal., 15, 419 431. | MR | Zbl

[12] R. Glowinski, A. Marrocco, 1975, Sur l'approximation par éléments finis d'ordre un, et la résolution, par pénalisation-dualite, d'une classe de problèmes de Dirichlet non linéaires, R.A.I.R.O. Analyse Numérique, 2, 41-64. | Numdam | MR | Zbl

[13] W. B. Liu, J. W. Barrett, 1993, A remark on the regulanty of the solutions of the p-Laplacian and its applications to their finite element approximation, J. Math. Anal. Appl., 178, 470-487. | MR | Zbl

[14] W. B. Liu, J. W. Barrett, 1993, A further remark on the regularity of the solutions of the p-Laplacian and its applications to their finite element approximation, Nonlinear Anal., 21, 379-387. | MR | Zbl

[15] W. B. Liu, J. W. Barrett, 1993, Higher order regularity for the solutions of some quasilinear degenerate elliptic equations in the plane, SIAM, J. Math. Anal., 24, 1522-1536. | MR | Zbl

[16] W. B. Liu, J. W. Barrett, Finite element approximation of some degenerate monotone quasilinear elliptic Systems, SIAM, J. Numer. Anal. (to appear). | MR | Zbl

[17]H. D. Mittelmann, 1978, On the approximate solution of nonlinear variation inequalities, Numer. Math., 29, 451-462. | MR | Zbl

[18] R. H. Nochetto, 1989, Pointwise accuracy of a finite element method for nonlinear variational inequalities, Numer. Math., 54, 601-618. | MR | Zbl

[19] J. R. Philip, 1961, N-diffusion, Aust. J. Phys., 14. 1-13. | MR | Zbl