On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
Hlaváček, Ivan ; Křížek, Michal
Applications of Mathematics, Tome 32 (1987), p. 131-154 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1987-01-01
Classification:  35J25,  65N15,  65N30,  73C99,  74S05 
@article{104242,
     author = {Ivan Hlav\'a\v cek and Michal K\v r\'\i \v zek},
     title = {On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition},
     journal = {Applications of Mathematics},
     volume = {32},
     year = {1987},
     pages = {131-154},
     zbl = {0622.65097},
     mrnumber = {0885758},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104242}
}

Hlaváček, Ivan; Křížek, Michal. On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition. Applications of Mathematics, Tome 32 (1987) pp. 131-154. http://gdmltest.u-ga.fr/item/104242/

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