Skip to main content
SpringerLink
Log in

Some A Posteriori Error Estimates of the Finite-Difference Streamline-Diffusion Method for Convection-Dominated Diffusion Equations

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

In this paper, some a posteriori error estimates of the finite-difference streamline-diffusion method for one- and two-dimensional time-dependent convection-dominated diffusion equations are presented, which can be used to reasonably adjust space mesh. Numerical results show that this method of local refinement is feasible and effective.

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. I. Babuska and T. Strouboulis, The Finite ElementMethod and its Reliability (Oxford University Press, 2001).

  2. I. Babuska and D.H. Yu, Asymptotically exact a posteriori error estimator for biquadratic elements, Finite Element in Analysis and Design 3 (1987) 341–354.

    Google Scholar 

  3. Z.M. Chen, R.H. Nochetto and A. Schmidt, A posteriori error control and adaptivity for a phase relaxation model (to appear).

  4. Z.M. Chen, R.H. Nochetto and A. Schmidt, A characteristic Galerkin method with adaptive error control for the continuous casting problem (to appear).

  5. Ph. Clément, Approximation by finite element functions using local regularization, RAIRO Anal. Numer. 2 (1975) 77–84.

    Google Scholar 

  6. K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems (I): A linear model problem, SIAM J. Numer. Anal. 28 (1991) 43–77.

    Google Scholar 

  7. K. Eriksson and C. Johnson, Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems, Math. Comp. 80 (1993) 167–188.

    Google Scholar 

  8. [8] K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems (II): Optimal error estimates in L∞(L 2 ), SIAM J. Numer. Anal. 32 (1995) 706–740.

    Google Scholar 

  9. T. Hughes, T. Tezduyar and A. Brooks, A new finite element formulation for computational fluid dynamics I-IV, Comput. Methods Appl. Mech. Engrg. 54 (1986) 223–234, 341–355; 58 (1986) 305–328, 329–336.

    Google Scholar 

  10. C. Johnson, U. Nävert and J. Pitkaranta, Finite element methods for linear hyperbolic problems, Comput. Methods Appl. Mech. Engrg. 45 (1984) 285–312.

    Google Scholar 

  11. C. Johnson and J. Saranen, Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations, Math. Comp. 47 (1986) 1–18.

    Google Scholar 

  12. T. Kang and D.H. Yu, A posteriori error estimate of FD-SD method for time-dependent convectiondominated diffusion equation and adjustment technique of space mesh, J. Numerical Methods Computer Applications 3 (2000) 194–207 (in Chinese).

    Google Scholar 

  13. C. Sun and H. Shen, Finite-Different Stream-Diffusion method for time-dependent convection-diffusion equation, Numer. Math., A Journal of Chinese University 1 (1998) 72–85.

    Google Scholar 

  14. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh Refinement Techniques (Wiley-Teubner, 1996).

  15. D.H. Yu, Asymptotically exact a posteriori error estimator for elements of bi-even degree, Chinese J. Numer. Math. Appl. 13(2) (1991) 64–78.

    Google Scholar 

  16. D.H. Yu, Asymptotically exact a posteriori error estimator for elements of bi-odd degree, Chinese J. Numer. Math. Appl. 13(4) (1991) 82–90.

    Google Scholar 

  17. D.H. Yu, The adaptive methods in the finite element and boundary element computation, Progr. Natur. Sci. 2 (1994) 142–148.

    Google Scholar 

  18. Q. Zhang and C. Sun, Finite difference-streamline diffusion method for nonlinear convectiondiffusion equation, Math. Numer. Sinica 20(2) (1998) 212–224.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100080, China

    Tong Kang & Dehao Yu

Authors
  1. Tong Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dehao Yu
    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

Kang, T., Yu, D. Some A Posteriori Error Estimates of the Finite-Difference Streamline-Diffusion Method for Convection-Dominated Diffusion Equations. Advances in Computational Mathematics 15, 193–218 (2001). https://doi.org/10.1023/A:1014294002686

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014294002686

Search

Navigation