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\(L^{\infty}\) error estimates and superconvergence results for a collocation-\(H^{-1}\)-Galerkin method for elliptic equations. (English) Zbl 0584.65073
The paper deals with a mixed approximation scheme based on a collocation method and an \(H^{-1}\) Galerkin procedure for solving general elliptic equations of the form \(\nabla \cdot (a\nabla u)+b\cdot \nabla u+cu=f\) in \(\Omega\), \(u=0\) on \(\partial \Omega\). The author establishes \(L^{\infty}\)-error estimates and proves that at particular points in the domain, the rate of convergence is higher than the global rate, i.e. some superconvergence phenomena occurs. Some numerical results are presented.
Reviewer: J.Haslinger

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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
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