## 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.

### 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 74S05 Finite element methods applied to problems in solid mechanics
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### References:

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