Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2013-09, Vol.249, p.74-94
Main Authors: Carstensen, C., Merdon, C.
Format: Article
Language:English
Subjects:
A posteriori error estimation
Adaptive finite element method
Crouzeix–Raviart finite element method
Nonconforming finite element method
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2012.12.021