Geodesic
On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
Applications of Mathematics, Tome 32 (1987) no. 2, pp. 131-154

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

Second order elliptic systems with Dirichlet boundary conditions are solved by means of affine finite elements on regular uniform triangulations. A simple averagign scheme is proposed, which implies a superconvergence of the gradient. For domains with enough smooth boundary, a global estimate $O(h^{3/2})$ is proved in the $L^2$-norm. For a class of polygonal domains the global estimate $O(h^2)$ can be proven.
DOI : 10.21136/AM.1987.104242
Classification : 35J25, 65N15, 65N30, 73C99, 74S05
Keywords: post-processing; averaged gradient; Galerkin method; system; finite elements; superconvergence; global estimate; elliptic systems 
@article{10_21136_AM_1987_104242,
     author = {Hlav\'a\v{c}ek, Ivan and K\v{r}{\'\i}\v{z}ek, Michal},
     title = {On a superconvergent finite element scheme for elliptic systems. {I.} {Dirichlet} boundary condition},
     journal = {Applications of Mathematics},
     pages = {131--154},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {1987},
     doi = {10.21136/AM.1987.104242},
     mrnumber = {0885758},
     zbl = {0622.65097},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104242/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
AU  - Křížek, Michal
TI  - On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
JO  - Applications of Mathematics
PY  - 1987
SP  - 131
EP  - 154
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104242/
DO  - 10.21136/AM.1987.104242
LA  - en
ID  - 10_21136_AM_1987_104242
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%A Křížek, Michal
%T On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
%J Applications of Mathematics
%D 1987
%P 131-154
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104242/
%R 10.21136/AM.1987.104242
%G en
%F 10_21136_AM_1987_104242
Hlaváček, Ivan; Křížek, Michal. On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition. Applications of Mathematics, Tome 32 (1987) no. 2, pp. 131-154. doi: 10.21136/AM.1987.104242

Cité par Sources :