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Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case
Author(s):
Alfred
H.
Schatz;
Lars
B.
Wahlbin.
Journal:
Math. Comp.
73
(2004),
517-523.
MSC (2000):
Primary 65N30, 65N15
Posted:
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,  , rather than for  itself. We also give a posteriori estimators for second derivatives on each element.
References:
-
- [1]
- A. Demlow, Piecewise linear finite elements methods are not localized, Math. Comp. (to appear).
- [2]
- K. Eriksson and C. Johnson, An adaptive finite element method for linear elliptic problems, Math. Comp. 50 (1988), 361-384. MR 89c:65119
- [3]
- W. Hoffmann, A. H. Schatz, L. B. Wahlbin and G. Wittum, Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part I: A smooth problem and globally quasi-uniform meshes, Math. Comp. 70 (2001), 897-909. MR 2002a:65178
- [4]
- A. H. Schatz, Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates, Math. Comp. 67 (1998), 877-899. MR 98j:65082
- [5]
- A. H. Schatz and L. B. Wahlbin, Pointwise error estimates for differences of piecewise linear finite element approximations, SIAM J. Numer. Anal. (to appear).
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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:
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
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
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