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Iteration method as discretization procedures

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1457)

Abstract

Much work has been done upon the fast solution of the linear systems arising from upwind difference and central difference approximations to convection dominated convection diffusion equations and yet neither scheme produces acceptable approximate solutions to the original boundary value problem. Still, if these two discretizations are combined via a defect correction approach one obtains an algorithm with many of the best features of both and for which the insights on the fast solution of the associated linear system are very useful. In this report, we describe the algorithm and summarize some of the authors' recent work which gives local error estimates in 2-D on a finite element implementation of this promising scheme.

Key Works

  • Convection-diffusion equation
  • defect correction method
  • interior estimates

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© 1990 Springer-Verlag

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Axelsson, O., Layton, W. (1990). Iteration method as discretization procedures. In: Axelsson, O., Kolotilina, L.Y. (eds) Preconditioned Conjugate Gradient Methods. Lecture Notes in Mathematics, vol 1457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090908

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  • DOI: https://doi.org/10.1007/BFb0090908

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53515-7

  • Online ISBN: 978-3-540-46746-5

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