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A posteriori error estimator for expanded mixed hybrid methods. (English) Zbl 1120.65120
The authors construct an error estimator for expanded hybrid finite-element methods for the second-order elliptic problem $$\align - \text{div}\left( K\nabla u\right) =0 &\quad\text{in }\Omega,\\ u=0\quad\text{ on }\Gamma ^D,\quad -K\nabla u\cdot {\bold n}=g^N &\quad\text{on }\Gamma ^N,\quad \partial \Omega =\overline{\Gamma }^D\cup \overline{\Gamma }^N. \endalign$$ An a posteriori error analysis yields reliable and efficient estimates based on residuals. It is proved that the a posteriori error estimator yields global upper bounds and local lower bounds on the error measured in the $ L^2$-norm, using duality techniques. Some numerical examples are presented to show the effectivity of error indicators on adaptive grid refinement.

65N15Error bounds (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
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