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.

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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.
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 
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     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},
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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. http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104242/

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