Abstract
In this paper, a new triangular element (Quasi-Carey element) is constructed by the idea of Specht element. It is shown that this Quasi-Carey element possesses a very special property, i.e., the consistency error is of order O(h 2), one order higher than its interpolation error when the exact solution belongs to H 3(Ω). However, the interpolation error and consistency error of Carey element are of order O(h). It seems that the above special property has never been seen for other triangular elements for the second order problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. F. Carey, An analysis of finite element equations and mesh subdivision, Comput. Methods Appl. Mech. Engrg., 1976, 9(2): 165–179.
Z. C. Shi, Convergence properties of two nonconforming finite elements, Comput. Methods Appl. Mech. Engrg., 1985, 48(2): 123–137.
Q. Lin and P. Luo, High-accuracy analysis for a nonconforming membrane element, J. Math. Study, 1995, 28(3): 1–5.
D. Y. Shi, S. C. Chen, and I. Hagiwara, Convergence analysis for a nonconforming membrane element on anisotropic meshes, J. Comput. Math., 2005, 23(4): 373–382.
P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
Z. C. Shi, A remark on the optimal order of convergence of Wilson nonconforming element, Math. Numer. Sinica, 1986, 8(2): 159–163.
Z. C. Shi, On the accuracy of the quasi-conforming and generalized conforming finite elements, Chinese Ann. Math. Ser. B, 1990, 11(2): 148–155.
D. Y. Shi and S. C. Chen, Accuracy analysis of 12-parameter rectangular plate elements with geometric symmetry, J. Syst. Sci. & Complexity, 2000, 13(2): 146–151.
S. C. Chen and D. Y. Shi, Accuracy analysis for Quasi-Wilson element, Acta Math. Sci., 2000, 20(1): 44–48.
Q. Lin and N. N. Yan, Construction and Analysis for Effective Finite Element Methods (in Chinese), Hebei University Press, Baoding, 1996.
Q. Lin and J. F. Lin, Finite Element Methods: Accuracy and Improvement, Mathematics Monograph Series 1, Science Press, Beijing, 2006.
B. Specht, Modified shape functions for the three-node plate bending element passing the patch test, Int. J. Numer. Methods Engrg., 1988, 26(3): 705–715.
D. Y. Shi and C. X. Wang, Anisotropic nonconforming finite element approximation to variational inequality problems with displacement obstacle (in Chinese), J. Engrg. Math., 2006, 23(3): 399–406.
D. Y. Shi, S. P. Mao, and H. Liang, Anisotropic biquadratic element with superclose result, J. Syst. Sci. & Complexity, 2006, 19(4): 566–576.
D. Y. Shi, H. Liang, and C. X. Wang, Superconvergence analysis of a nonconforming triangular element on anisotropic meshes, J. Syst. Sci. & Complexity, 2007, 20(4): 536–544.
Author information
Authors and Affiliations
Corresponding author
Additional information
*This research is supported by the National Natural Science Foundation of China under Grant No. 10671184.
Rights and permissions
About this article
Cite this article
Shi, D., Hao, X. ACCURACY ANALYSIS FOR QUASI-CAREY ELEMENT*. J Syst Sci Complex 21, 456–462 (2008). https://doi.org/10.1007/s11424-008-9127-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-008-9127-5