Abstract
We consider the first boundary value problem of the second order elliptic equation and serendipity rectangular elements. Papers [2,3,9] proved that the gradients of finite element solution possess superconvergence at Gaussianpoint. In this paper, we extend the results in papers [2,3,9] in the sense that the coefficients of the elliptic equations are discontinuous on a curve S which lies in the bounded domain Ω.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chen Chuan-mao. Optimal points of the stresses for triangular linear element.Numerical Mathematics of Chinese University,2 (1980), 12–20, (in Chinese)
Zlamal, M., Some superconvergence results in the finite element method.Lecture Notes in Mathematics.606 (1977) 353–362.
Zlamal, M., Superconvergence and reduced integration in the finite element method.Math. Comp.,32 (1978), 663–685.
Ciarlet, P. G. and P. A. Raviart, General Lagrange and Hermite interpolation in Rn with applications to finite element methods.Arch. Rat. Mech. Anal. 46 (1972), 177–199.
Zienkiewicz, O. C.,The Finite Element Method in Engineering Science, Mc-Graw Hill, London (1977).
Ciarlet, P.,The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam (1978).
Chen Chuan-miao.The Finite Element Mechod and the Analysis for Raising Accuracy Hunan Scientific and Technical Publishing House (1982). (in Chinese)
Adams, R. A.:Sobolev Spaces, Academic Press, New York (1975).
Chen Chuan-miao. Superconvergence of finite element solutions and its derivatives,Numerical Mathematics of Chinese University.3 (1981). 118–125. (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by Li Hao
Rights and permissions
About this article
Cite this article
Xiao-fan, H. The optimal point of the gradient of finite element solution. Appl Math Mech 7, 785–794 (1986). https://doi.org/10.1007/BF01900611
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01900611