Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations

Abstract : We present equilibrated flux a posteriori error estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed finite element discretizations of the two-dimensional Poisson problem. Relying on the equilibration by mixed finite element solution of patchwise Neumann problems, the estimates are guaranteed, locally computable, locally efficient, and robust with respect to polynomial degree. Maximal local overestimation is guaranteed as well. Numerical experiments suggest asymptotic exactness for the incomplete interior penalty discontinuous Galerkin scheme.
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SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.1058-1081. 〈http://epubs.siam.org/doi/10.1137/130950100〉. 〈10.1137/130950100〉
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Alexandre Ern, Martin Vohralík. Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.1058-1081. 〈http://epubs.siam.org/doi/10.1137/130950100〉. 〈10.1137/130950100〉. 〈hal-00921583v2〉

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