Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 

 

Error estimates for 3-$\mathrm{d}$ narrow finite elements


Author: Ricardo G. Durán
Journal: Math. Comp. 68 (1999), 187-199
MSC (1991): Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-99-00994-1
MathSciNet review: 1489970
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We obtain error estimates for finite element approximations of the lowest degree valid uniformly for a class of three-dimensional narrow elements. First, for the Lagrange interpolation we prove optimal error estimates, both in order and regularity, in $L^{p}$ for $p>2$. For $p=2$ it is known that this result is not true. Applying extrapolation results we obtain an optimal order error estimate for functions sligthly more regular than $H^{2}$. These results are valid both for tetrahedral and rectangular elements. Second, for the case of rectangular elements, we obtain optimal, in order and regularity, error estimates for an average interpolation valid for functions in $W^{1+s,p}$ with $1\le p\le \infty $ and $0\le s\le 1$.


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


Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 65N30

Retrieve articles in all journals with MSC (1991): 65N30


Additional Information

Ricardo G. Durán
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina

DOI: https://doi.org/10.1090/S0025-5718-99-00994-1
Received by editor(s): May 1, 1995
Received by editor(s) in revised form: May 27, 1997
Article copyright: © Copyright 1999 American Mathematical Society