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A posteriori error estimates with post-processing for nonconforming finite elements. (English) Zbl 1041.65083

An a posteriori error estimators for nonconforming finite elements (FEs) for second order elliptic problems derived by using the “post-processed” error between the original solution of a nonconforming finite element method and a computable conforming approximation of that solution. Using the fact that the nonconforming FE space contains the conforming FE space of the first order, valid for many nonconforming elements, the presented analysis is based on the existing theory for conforming methods and some additional arguments. Local lower and global upper a posteriori error bounds are established. Other possible applications are discussed as well.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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