Advertisement

An introduction to the Finite Element Method

  • J. J. I. M. van Kan
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 81)

Abstract

The finite element method (FEM) has grown from a civil engineering tool into a general method for solving partial differential equations. In this area it beats its competitors: the finite difference method (FDM) and the finite volume method (FVM), in that it is better suited to deal with complex geometries and difficult boundary conditions. As opposed to that, it usually is more difficult to apply and the resulting sets of equations have a more complicated structure.

Keywords

Finite Element Method Finite Difference Method Nodal Point Finite Volume Method Target Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Becker, E.B., G.F. Carey, J. Tinsley Oden Finite Elements .Vols I-VII Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1981–1984.Google Scholar
  2. Ciarlet, P.G. Finite element methods for elliptic problems .North Holland Publishing Co, Amsterdam, 1986.Google Scholar
  3. Cuthill, E., J. McKee Reducing the bandwidth of sparse symmetric matrices . Proc. ACM Nat. Conf., New York 1969, 157–172.Google Scholar
  4. Cuvelier, C., A. Segal, A.A van Steenhoven Finite element method and Navier Stokes equations . D. Reidel Publishing Company, Dordrecht, 1986.CrossRefGoogle Scholar
  5. Hinton, E., D.R.J. Owen Finite element programming . Academic Press, New York, 1977.Google Scholar
  6. Hughes, Thomas J.R. The Finite Element Method . Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1987.zbMATHGoogle Scholar
  7. Kikuchi, N. Finite element methods in mechanics .Cambridge University Press, Cambridge, 1986.zbMATHCrossRefGoogle Scholar
  8. Meijerink, J.A., H.A. van der Vorst An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix . Math. Comp. 31 148–162, 1977.MathSciNetzbMATHGoogle Scholar
  9. Mitchell, A.R., R. Wait The finite element method in partial differential equations . John Wiley, New York, 1977.zbMATHGoogle Scholar
  10. Strang, G., G.J. Fix An analysis of the finite element method . Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1973.zbMATHGoogle Scholar
  11. Zienkiewicz, O.C. The finite element method in engineering science . McGraw-Hill, New York, 1971.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • J. J. I. M. van Kan
    • 1
  1. 1.Faculty of Technical Mathematics and InformaticsDelft University of TechnologyDelftThe Netherlands

Personalised recommendations