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Derivative superconvergent points in finite element solutions of harmonic functions-- A theoretical justification
Author(s):
Zhimin
Zhang.
Journal:
Math. Comp.
71
(2002),
1421-1430.
MSC (2000):
Primary 65N30
Posted:
December 5, 2001
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Abstract:
Finite element derivative superconvergent points for harmonic functions under local rectangular mesh are investigated. All superconvergent points for the finite element space of any order that is contained in the tensor-product space and contains the intermediate family can be predicted. In the case of the serendipity family, results are given for finite element spaces of order below 6. The results justify the computer findings of Babuska, et al.
References:
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- I. Babuska and T. Strouboulis, The Finite Element Method and its Reliability, Oxford University Press, London, 2001.
- 2.
- I. Babuska, T. Strouboulis, C.S. Upadhyay, and S.K. Gangaraj, Computer-based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace's, Poisson's, and the elasticity equations, Numer. Methods Partial Differential Equations 12 (1996), 347-392. MR 97c:65160
- 3.
- M. Krízek, P. Neittaanmäki, and R. Stenberg (Eds.), Finite element methods. Superconvergence, post-processing, and a posteriori estimates, Lecture Notes in Pure and Applied Mathematics Series, Vol. 196, Marcel Dekker, New York, 1997. MR 98i:65003
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- N.N. Lebedev, Special functions and their applications, Dover, New York, 1972. MR 50:2568
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- A.H. Schatz, I.H. Sloan, and L.B. Wahlbin, Superconvergence in finite element methods and meshes which are symmetric with respect to a point, SIAM J. Numer. Anal. 33(2) (1996), 505-521. MR 98f:65112
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- L.B. Wahlbin, Superconvergence in Galerkin finite element methods, Lecture Notes in Mathematics, Vol. 1605, Springer, Berlin, 1995. MR 98j:65083
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- Zhimin Zhang, Derivative superconvergent points in finite element solutions of Poisson's equation for the serendipity and intermediate families--A theoretical justification, Math. Comp. 67 (1998), 541-552. MR 98i:65104
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Additional Information:
Zhimin
Zhang
Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email:
zzhang@math.wayne.edu
DOI:
10.1090/S0025-5718-01-01398-9
PII:
S 0025-5718(01)01398-9
Keywords:
Superconvergence,
finite element,
harmonic function
Received by editor(s):
November 21, 2000
Posted:
December 5, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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