nonconforming Crouzeix Raviart finite element method guaranteed error control a posteriori error estimators Poisson problem partial differential equations equilibration error estimators inhomogeneous boundary conditions Computational Survey On A Posteriori Error Estimators for Nonconforming Finite Element Methods for the Poisson Problem Carsten Carstensen Carstensen Carsten Christian Merdon Merdon Christian Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

Computational Survey On A Posteriori Error Estimators for Nonconforming Finite Element Methods for the Poisson Problem

Carsten Carstensen , Christian Merdon

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65N15 Error bounds

Abstract
This paper compares different a posteriori error estimators for nonconforming first-order Crouzeix-Raviart finite element methods for simple second-order partial differential equations. All suggested error estimators yield a guaranteed upper bound of the discrete energy error up to oscillation terms with explicit constants. Novel equilibration techniques and an improved interpolation operator for the design of conforming approximations of the discrete nonconforming finite element solution perform very well in an error estimator competition with six benchmark examples.

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