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Optimal \(L^{\infty}\)-error estimates for nonconforming and mixed finite element methods of lowest order. (English) Zbl 0597.65080
For second order linear elliptic problems it is proved that the \(P_ 1\)- nonconforming finite element method has the same \(L^{\infty}\)- asymptotic accuracy as the \(P_ 1\)-conforming one. This result is applied to derive optimal \(L^{\infty}\)-error estimates for both the displacement and the stress fields of the lowest order Raviart-Thomas mixed finite element method, and a superconvergence result at the barycenter of each element.

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
74S05 Finite element methods applied to problems in solid mechanics
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