Geodesic
Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries
Applications of Mathematics, Tome 29 (1984) no. 1, pp. 52-69.

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

Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined. A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The internal approximation can be obtained by solving a system of linear algebraic equations with a positive definite matrix.
DOI : 10.21136/AM.1984.104068
Classification : 35J25, 65N30
Keywords: dual variational methods; stream function; finite element; piecewise smooth boundary; dual problem; optimal rate of convergence 
@article{10_21136_AM_1984_104068,
     author = {Hlav\'a\v{c}ek, Ivan and K\v{r}{\'\i}\v{z}ek, Michal},
     title = {Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries},
     journal = {Applications of Mathematics},
     pages = {52--69},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {1984},
     doi = {10.21136/AM.1984.104068},
     mrnumber = {0729953},
     zbl = {0543.65074},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104068/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
AU  - Křížek, Michal
TI  - Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries
JO  - Applications of Mathematics
PY  - 1984
SP  - 52
EP  - 69
VL  - 29
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104068/
DO  - 10.21136/AM.1984.104068
LA  - en
ID  - 10_21136_AM_1984_104068
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%A Křížek, Michal
%T Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries
%J Applications of Mathematics
%D 1984
%P 52-69
%V 29
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104068/
%R 10.21136/AM.1984.104068
%G en
%F 10_21136_AM_1984_104068
Hlaváček, Ivan; Křížek, Michal. Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries. Applications of Mathematics, Tome 29 (1984) no. 1, pp. 52-69. doi : 10.21136/AM.1984.104068. http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104068/

Cité par Sources :