FoCM 2014 conference
Workshop A5 - Multiresolution and Adaptivity in Numerical PDEs
December 12, 18:00 ~ 18:40 - Room B22
Polynomial-degree-robust a posteriori estimates in a unified setting
Martin Vohralik
INRIA Paris-Rocquencrourt, France - martin.vohralik@inria.fr
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.
Joint work with Alexandre Ern (CERMICS, Universite Paris-Est, France).