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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