Superconvergent recoveries of carey non-conforming element approximations

Communications in Numerical Methods in Engineering

Volumn 13, Issue 6, 1997, Pages 439-452

  Zhang, Lin ^a,b   Li, Likang ^a  

^a FUDAN UNIVERSITY   (China)

^b UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY   (China)

Author keywords

Non conforming finite elements; Superconvergence

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; PIECEWISE LINEAR TECHNIQUES;

CAREY NONCONFORMING ELEMENT APPROXIMATION;

FINITE ELEMENT METHOD;

EID: 0031167889     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-0887(199706)13:6<439::AID-CNM71>3.0.CO;2-R     Document Type: Article

References (23)

1. M. Křížek and P. Neittaanmäki, 'On superconvergence techniques', Acta Appl. Math., 9, 175-198 (1987).
2. M. Křížek, 'Superconvergence phenomena in the finite element method', Comput. Methods Appl. Eng., 116, 157-163 (1994).
3. L. B. Wahlbin, 'Local behaviour in finite element methods', in Handbook of Numerical Analysis, Vol. II, P. G. Ciarlet and J. L. Lions (eds.), North-Holland, Amsterdam, 1991, pp. 352-522.
4. J. R. Whiteman and G. Goodsell, 'A survey of gradient superconvergence for finite element approximations to second order elliptic problems on triangular and tetrahedral meshes', Proc. MAFELAP VII, Academic Press, London, 1991, pp. 55-74.
5. J. R. Whiteman and G. Goodsell, 'Some gradient superconvergence results in the finite element method', Lect. Notes Math. 1397, P. R. Turner (ed.), Springer, Berlin, 1989, pp. 182-260.
6. C. M. Chen, Finite Element Method and Its Analysis in Improving Accuracy, Hunan Science and Technology Publishers, Hunan, 1982 (in Chinese).
7. C. M. Chen and Y. Q. Huang, High Accuracy Theory of Finite Element Methods, Hunan Science and Technology Publishers, Hunan, 1995 (in Chinese).
8. Q. D. Zhu and Q. Lin, Superconvergence Theory of Finite Element Method, Hunan Science and Technology Publishers, Hunan, 1989 (in Chinese).
9. H. Wang, 'On the superconvergence estimate of Wilson element', J. Shandong Univ. (Natural Sciences) , 21(4), 89-95 (1986) (in Chinese).
10. H. S. Chen and B. Li, 'Superconvergence analysis and error expansion for the Wilson nonconforming finite element', Numer. Math., 69, 125-140 (1994).
11. Z. C. Shi and B. Jiang, 'A new superconvergence property of Wilson nonconforming finite element', preprint.
12. G. F. Carey, 'An analysis of finite element equations and mesh subdivisions', Comput. Meth. Appl. Mech. Eng., 9, 165-179 (1976).
13. Zhong-ci SHI, 'Convergence properties of two nonconforming finite elements', Comput. Methods Appl. Mech. Eng., 48, 123-137 (1985).
14. Q. P. Deng, 'Error estimates of a nonconforming membrane element and its application for obstacle problem', J. Suzhou Univ. (Natural Science) 5(1), 34-39 (1989) (in Chinese).
15. P. Luo, 'Superconvergence estimates for a nonconforming membrane element', Northeastern Math. J., 8(4), 477-482 (1992).
16. Q. Lin and P. Luo, 'High accuracy analysis for a nonconforming membrane element', Math. Study, 28(3), 1-5 (1995).
17. Q. Lin and J. C. Xu, 'Linear finite elements with high accuracy', J. Comput. Math., 3(2), 115-133 (1985).
18. M. Křížek and P. Neittaanmäki, 'Superconvergence phenomenon in the finite element method arising from averaging gradients', Numer. Math., 45, 105-116 (1984).
19. M. Křížek and P. Neittaanmäki, 'On a global superconvergence of the gradient of linear triangular elements', J. Comput. Appl. Math., 18, 221-233 (1987).
20. N. Levine, 'Superconvergent recovery of the gradient from piecewise linear finite element approximations', IM A J. Numer. Anal., 5, 407-427 (1985).
21. P. Neittaanmäki and M. Křížek, 'Superconvergence of the finite element schemes arising from the use of averaged gradients', Accuracy Estimates and Adaptive Refinements in Finite Element Computations, Proc. Int. Conf., Lisbon, 1984, pp. 169-178.
22. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
23. R. Rannacher and R. Scott, 'Some optimal error estimates for piecewise linear finite element approximations', Math. Comput., 38, 437-445 (1982).