Skip to main content
SpringerLink
Log in

The numerical solutions of interface problems by infinite element method

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary

In this paper we derive error estimates for infinite element method used in the approximation of solutions of interface problems. Furthermore, approximations of stress intensity factors are given. The infinite element method may be considered as a certain scheme of mesh refinement, but it has the advantages that the refinement is easy to be constructed that the stiffness matrix can be calculated efficiently, and that an approximate solution which has a singularity at the singular point can be also obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Babuška, I.: Singularities problem in the finite element method. Tech. Note BN-835, Institut for Fluid Dynamics and Applied Mathematics. University of Maryland, 1976

  2. Babuška, I.: Solution of Problems with Interface and Singularities. Tech. Note BN-789, Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, 1974

  3. Kellogg, R.B.: Singularities in Interface problems. Numerical Solution of Partial Differential Equations II, (B. Hubbard, Ed.) New York: Academic Press 1971

    Google Scholar 

  4. Kellogg, R.B.: On the Poisson Equation with Intersecting Interfaces. Applicable Anal.4, 101–129 (1975)

    Google Scholar 

  5. Babuška, I., Kellogg, R.B., Pitkäranta, J.: Direct and Inverse Error Estimates for Finite Elements with Mesh Refinements. Numer. Math.33, 447–471 (1979)

    Google Scholar 

  6. Ying, L.: The Infinite Similar Element Method for Calculating Stress Intensity Factors. Sci. Sinica,XXI, 19–43 (1978)

    Google Scholar 

  7. Han, H., Ying, L.: An Iterative Method in the Infinite Element. Mathematicae Numericae Sinica,1, 91–99 (1979)

    Google Scholar 

  8. Ying, L.: On the Convergence of Infinite Similar Element Method. Acta Math. Appl. Sinica, 2,2, 149–166 (1979)

    Google Scholar 

  9. Thatcher, R.W.: The use of infinite grid refinements at singularities in the solution of Laplace's equation. Numer. Math.25, 163–178 (1976)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742 MD, College Park, Maryland, USA

    Houde Han

  2. Department of Mathematics, Peking University, The People's Republic of China

    Houde Han

Authors
  1. Houde Han
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Han, H. The numerical solutions of interface problems by infinite element method. Numer. Math. 39, 39–50 (1982). https://doi.org/10.1007/BF01399310

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01399310

Subject Classifications

Search

Navigation