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Equilibrated error estimators for discontinuous Galerkin methods. (English) Zbl 1160.65056
The authors consider an elliptic second order boundary value problem with nonhomogeneous mixed boundary conditions in two and three dimensions. These problems are approximated by a discontinuous Galerkin approximation and the authors propose a new a posteriori error estimator based on H(div)-conforming elements. They show that this estimator gives rise to an upper bound where the constant is one up the higher order terms; the lower bound is established with a constant depending on the aspect ratio of the mesh. The authors test the reliability and efficiency of the estimator through numerical tests.

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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