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Robust a posteriori error estimation for the nonconforming Fortin-Soulie finite element approximation
Author(s):
Mark
Ainsworth;
Richard
Rankin.
Journal:
Math. Comp.
77
(2008),
1917-1939.
MSC (2000):
Primary 65N15, 65N30
Posted:
April 28, 2008
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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.
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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:
10.1090/S0025-5718-08-02116-9
PII:
S 0025-5718(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
Posted:
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.
Copyright of article:
Copyright
2008,
American Mathematical Society
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