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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case


Authors: Alfred H. Schatz and Lars B. Wahlbin
Journal: Math. Comp. 73 (2004), 517-523
MSC (2000): Primary 65N30, 65N15
Published electronically: June 17, 2003
MathSciNet review: 2028417
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Abstract: We extend results from Part I about estimating gradient errors elementwise a posteriori, given there for quadratic and higher elements, to the piecewise linear case. The key to our new result is to consider certain technical estimates for differences in the error, $e(x_{1})-e(x_{2})$, rather than for $e(x)$ itself. We also give a posteriori estimators for second derivatives on each element.


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Additional Information

Alfred H. Schatz
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: schatz@math.cornell.edu

Lars B. Wahlbin
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: wahlbin@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01570-9
PII: S 0025-5718(03)01570-9
Received by editor(s): April 12, 2002
Received by editor(s) in revised form: September 7, 2002
Published electronically: June 17, 2003
Additional Notes: Both authors were supported by the National Science Foundation, USA, Grant DMS-0071412. They thank a referee for suggesting improvements in the presentation
Article copyright: © Copyright 2003 American Mathematical Society