Nonlinear Advection Problems and Overlapping Schwarz Waveform Relaxation

  • Martin J. Gander
  • Christian Rohde
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


We analyze the convergence behavior of the overlapping Schwarz waveform relaxation algorithm applied to nonlinear advection problems. We show for Burgers' equation that the algorithm converges super-linearly at a rate which is asymptotically comparable to the rate of the algorithm applied to linear advection problems. The convergence rate depends on the overlap and the length of the time interval. We carefully track dependencies on the viscosity parameter and show the robustness of all estimates with respect to this parameter.


Heat Kernel Domain Decomposition Domain Decomposition Method Viscosity Parameter Relaxation Algorithm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Martin J. Gander
    • 1
  • Christian Rohde
    • 2
  1. 1.Department of Mathematics and StatisticsMcGill University MontrealMontreal
  2. 2.Mathematisches InstitutAlbert-Ludwigs-Universität FreiburgFreiburg

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