Skip to main content
SpringerLink
Log in

A finite difference scheme for an interface problem

  • Original Paper
  • Area 2
  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

We propose a new finite difference scheme for an interface problem with piecewise constant coefficients. We use the Newton polynomial and continuity of flux to obtain finite difference scheme of second-order accuracy at the interface. We give several examples which show that the numerical solutions have O(h 2) accuracy.

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. Davis P.J.: Interpolation and Approximation. Dover Publications, Mineola (1975)

    MATH  Google Scholar 

  2. Gaveau, B., Okada, M., Okada, T.: Explicit heat kernels on graphs and spectral analysis. Several complex variables (Stockholm, 1987/1988). In: Mathematical Notes, vol. 38, pp. 364–388. Princeton University Press, Princeton (1993)

  3. LeVeque, R.J.: Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. SIAM (2007)

  4. LeVeque R.J., Li Z.: The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31(4), 1019–1044 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Li, Z., Ito, K.: The immersed interface method–numerical solutions of PDEs involving interface and irregular domains. In: SIAM Frontiers in Applied Mathematics (2006)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Tokyo, 192-0397, Japan

    Yingying Wu, Simon Truscott & Masami Okada

Authors
  1. Yingying Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Simon Truscott
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masami Okada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yingying Wu.

About this article

Cite this article

Wu, Y., Truscott, S. & Okada, M. A finite difference scheme for an interface problem. Japan J. Indust. Appl. Math. 27, 239–262 (2010). https://doi.org/10.1007/s13160-010-0004-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13160-010-0004-y

Keywords

Search

Navigation