Paper Info
Title
Guaranteed Energy Error Estimators for a Modified Robust Crouzeix-Raviart Stokes Element.
Abstract
This paper provides guaranteed upper energy error bounds for a modified lowest-order nonconforming Crouzeix–Raviart finite element method for the Stokes equations. The modification from Linke (Comput Methods Appl Mech Eng 268:782–800, 2014) is based on the observation that only the divergence-free part of the right-hand side should balance the vector Laplacian. The new method has optimal energy error estimates and can lead to errors that are smaller by several magnitudes, since the estimates are pressure-independent. An efficient a posteriori velocity error estimator for the modified method also should involve only the divergence-free part of the right-hand side. Some designs to approximate the Helmholtz projector are compared and verified by numerical benchmark examples. They show that guaranteed error control for the modified method is possible and almost as sharp as for the unmodified method.
Year
DOI
Venue
2015
10.1007/s10915-014-9943-9
Journal of Scientific Computing
Keywords
DocType
Volume
Mixed finite element methods, A posteriori error estimators, Stokes problem, Crouzeix–Raviart finite element methods, Divergence-free methods
Journal
64
Issue
ISSN
Citations 
2
1573-7691
0
PageRank 
References 
Authors
0.34
5
2
Name
Order
Citations
PageRank
Alexander Linke19212.29
Christian Merdon2627.33