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Energy norm a posteriori error estimates for mixed finite element methods


Authors: Carlo Lovadina and Rolf Stenberg
Journal: Math. Comp. 75 (2006), 1659-1674
MSC (2000): Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-06-01872-2
Published electronically: June 26, 2006
MathSciNet review: 2240629
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Abstract: This paper deals with the a posteriori error analysis of mixed finite element methods for second order elliptic equations. It is shown that a reliable and efficient error estimator can be constructed using a postprocessed solution of the method. The analysis is performed in two different ways: under a saturation assumption and using a Helmholtz decomposition for vector fields.


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Additional Information

Carlo Lovadina
Affiliation: Dipartimento di Matematica, Università di Pavia and IMATI-CNR, VIa Ferrata 1, Pavia 27100, Italy
Email: carlo.lovadina@unipv.it

Rolf Stenberg
Affiliation: Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 TKK, Finland
Email: rolf.stenberg@tkk.fi

DOI: https://doi.org/10.1090/S0025-5718-06-01872-2
Keywords: Mixed finite element methods, a posteriori error estimates, postprocessing.
Received by editor(s): October 20, 2004
Received by editor(s) in revised form: June 7, 2005
Published electronically: June 26, 2006
Additional Notes: This work has been supported by the European Project HPRN-CT-2002-00284 “New Materials, Adaptive Systems and their Nonlinearities. Modelling, Control and Numerical Simulation”.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.