Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Robust a posteriori error estimation for the nonconforming Fortin-Soulie finite element approximation


Authors: Mark Ainsworth and Richard Rankin
Journal: Math. Comp. 77 (2008), 1917-1939
MSC (2000): Primary 65N15, 65N30
DOI: https://doi.org/10.1090/S0025-5718-08-02116-9
Published electronically: April 28, 2008
MathSciNet review: 2429869
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We obtain a computable a posteriori error bound on the broken energy norm of the error in the Fortin-Soulie finite element approximation of a linear second order elliptic problem with variable permeability. This bound is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the error.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65N15, 65N30

Retrieve articles in all journals with MSC (2000): 65N15, 65N30


Additional Information

Mark Ainsworth
Affiliation: Department of Mathematics, Strathclyde University, 26 Richmond Street, Glasgow G1 1XH, Scotland
Email: M.Ainsworth@strath.ac.uk

Richard Rankin
Affiliation: Department of Mathematics, Strathclyde University, 26 Richmond Street, Glasgow G1 1XH, Scotland
Email: rs.rran@maths.strath.ac.uk

DOI: https://doi.org/10.1090/S0025-5718-08-02116-9
Keywords: Robust a posteriori error estimation, nonconforming finite element, Fortin--Soulie element.
Received by editor(s): October 10, 2006
Received by editor(s) in revised form: April 5, 2007
Published electronically: April 28, 2008
Additional Notes: Partial support of the first author by the Engineering and Physical Sciences Research Council of Great Britain under grant GR/S35101 and of the second author through a research studentship is gratefully acknowledged.
Article copyright: © Copyright 2008 American Mathematical Society