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On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition. (English) Zbl 0622.65097
A system of linear second order elliptic equations with Dirichlet boundary conditions in a bounded plane region is approximated by an averaging scheme based on linear finite elements. The scheme guarantees superconvergence of the derivatives of the Galerkin solution. For domains with enough smoothness on the boundary a global estimate $$O(h^{3/2})$$ is established in the $$L^ 2$$ norm. For a class of polygonal domains the global estimate $$O(h^ 2)$$ is found.
Reviewer: W.Ames

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 74S05 Finite element methods applied to problems in solid mechanics
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