Discretization and Iterative Solution of Convection Diffusion Equations

  • R. Kornhuber
  • G. Wittum
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


We propose an extended box method which turns out to be a variant of standard finite element methods in the case of pure diffusion and an extension of backward differencing to irregular grids if only convective transport is present. Together with the adaptive orientation proposed in a recent paper and a streamline ordering of the unknowns, this discretization leads to a highly efficient adaptive method for the approximation of internal layers in the case of large local Peclet numbers.


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  1. [1]
    R.E. Bank, D.E. Rose: Some Error Estimates for the Method. SLAM J. Numer. Anal. 24 No. 4, p. 777–787 (1987).CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    P. Deuflhard, P. Leinen and H. Yserentant: Concepts of an Adaptive Hierarchical Finite Element Code. IMPACT 1, p. 3–35 (1989).Google Scholar
  3. [3]
    W. Hackbusch: On First and Second Order Box Schemes. Computing 41, p. 277–296 (1989).CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    C. Johnson: Numerical Solutions of Partial Differential Equations by the Finite Element Method. Cambridge University Press, Cambridge (1987).Google Scholar
  5. [5]
    R. Kornhuber, R. Roitzsch: On Adaptive Grid Refinement in the Presence of Internal or Boundary Layers. IMPACT 2, p. 40–72 (1990).Google Scholar
  6. [6]
    P. Leinen: Ein schneller, adaptiver Löser für elliptische Randwertprobleme auf Seriell und Parallelrechnern. Thesis, University of Dortmund (1990),zbMATHGoogle Scholar
  7. [7]
    R. Roitzsch: KASKADE Users Manual. Technical Report TR 89–4, Konrad-Zuse-Zentrum Berlin (ZIB) (1989).Google Scholar
  8. [8]
    R. Roitzsch: KASKADE Programmer’s Manual. Technical Report TR 89–5, Konrad-Zuse-Zentrum Berlin (ZIB) (1989).Google Scholar
  9. [9]
    G. Wittum: On the Robustness of ILU-Smoothing. SIAM J. Sci. Stat. Comput. 10, p. 699–717 (1989).CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1993

Authors and Affiliations

  • R. Kornhuber
    • 1
  • G. Wittum
    • 2
  1. 1.Konrad-Zuse-Zentrum für Informationstechnik BerlinBerlin 31Fed. Rep. of Germany
  2. 2.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergFed. Rep. of Germany

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