Science in China Series A: Mathematics

, Volume 47, Supplement 1, pp 136–145 | Cite as

Superconvergence and asymptotic expansions for linear finite element approximations on crisscross mesh

Article
  • 36 Downloads

Abstract

In this paper, we discuss the error estimation of the linear finite element solution on criss-cross mesh. Using space orthogonal decomposition techniques, we obtain an asymptotic expansion and superconvergence results of the finite element solution. We first prove that the asymptotic expansion has different forms on the two kinds of nodes and then derive a high accuracy combination formula of the approximate derivatives.

Keywords

criss-cross mesh linear finite element superconvergence 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chen Chuanmiao, Huang Yunqing, High Accuracy Theory of FEM (in Chinese), Changsha: Hunan Science and Technology Press, 1995.Google Scholar
  2. 2.
    Goodsell, G., Whiteman, J. R., A unified treatment of superconvergent recovered gradient functions for piecewise linear finite element approximations, Internat. J. Numer. Methods Engrg., 1989, 27: 469–481.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Lin Qun and Yan Ningning, The Construction and Analysis of High Efficient Finite Element Methods, Baoding: Hebei University Press, June, 1996.Google Scholar
  4. 4.
    Krizek, M., Neittaanmaki, P., On a global superconvergence of the gradient of linear triangular elements, J. Comput. Appl. Math., 1987, 45: 221–233.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Schatz, A. H., Sloan, I. H., Wahlbin, L. B., Superconvergence in finite elelment methods and meshes which are symmetric with respect to a point, SIAM Journal on Numerical Analysis, 1996, 33(2): 505–521.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Wahlbin, L. B., Superconvergence in Galerkin Finite Methods, Lecture Notes in Mathematics, 1605, Berlin-Heidelberg: Springer-Verlag, 1995.MATHGoogle Scholar
  7. 7.
    Babuska, I., Strouboulis, T., Upadhyay, C. S. et al., Computer-based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutious of Laplace’s, Poisson’s, and the elasticity equations, Numer. Methods for PDEs, 1996, 12: 347–392.MATHMathSciNetGoogle Scholar
  8. 8.
    Babuska, I., Strouboulis, T., FEM-latest developments, open problems and perspective, International Colloquium on Applications of Computer Science and Mathematics in Architecture and Civil Engineering Weimar, Germany, February 26-March, 1997, 1.Google Scholar

Copyright information

© Science in China Press 2004

Authors and Affiliations

  1. 1.Department of MathematicsXiangtan UniversityXiangtanChina

Personalised recommendations