Geodesic
Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type
Applications of Mathematics, Tome 41 (1996) no. 6, pp. 467-478.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree $k\ge 1$ we prove the optimal rates of convergence $\mathcal O(h^k)$ in the $H^1$-norm and $\mathcal O(h^{k+1})$ in the $L^2$-norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account.
DOI : 10.21136/AM.1996.134338
Classification : 35J65, 65N30, 74A15
Keywords: nonlinear boundary value problem; finite elements; rate of convergence; anisotropic heat conduction 
@article{10_21136_AM_1996_134338,
     author = {Liu, Liping and K\v{r}{\'\i}\v{z}ek, Michal and Neittaanm\"aki, Pekka},
     title = {Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type},
     journal = {Applications of Mathematics},
     pages = {467--478},
     publisher = {mathdoc},
     volume = {41},
     number = {6},
     year = {1996},
     doi = {10.21136/AM.1996.134338},
     mrnumber = {1415252},
     zbl = {0870.65096},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134338/}
}
TY  - JOUR
AU  - Liu, Liping
AU  - Křížek, Michal
AU  - Neittaanmäki, Pekka
TI  - Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type
JO  - Applications of Mathematics
PY  - 1996
SP  - 467
EP  - 478
VL  - 41
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134338/
DO  - 10.21136/AM.1996.134338
LA  - en
ID  - 10_21136_AM_1996_134338
ER  - 
%0 Journal Article
%A Liu, Liping
%A Křížek, Michal
%A Neittaanmäki, Pekka
%T Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type
%J Applications of Mathematics
%D 1996
%P 467-478
%V 41
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134338/
%R 10.21136/AM.1996.134338
%G en
%F 10_21136_AM_1996_134338
Liu, Liping; Křížek, Michal; Neittaanmäki, Pekka. Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type. Applications of Mathematics, Tome 41 (1996) no. 6, pp. 467-478. doi : 10.21136/AM.1996.134338. http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134338/

Cité par Sources :