A Parareal in Time Semi-implicit Approximation of the Navier-Stokes Equations

  • Paul F. Fischer
  • Frédéric Hecht
  • Yvon Maday
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


The “parareal in time” algorithm introduced in Lions et al. [2001] enables parallel computation using a decomposition of the interval of time integration. In this paper, we adapt this algorithm to solve the challenging Navier-Stokes problem. The coarse solver, based on a larger timestep, may also involve a coarser discretization in space. This helps to preserve stability and provides for more significant savings.


Domain Decomposition Method Parareal Scheme Spectral Element Method Richardson Extrapolation Spectral Degree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Paul F. Fischer
    • 1
  • Frédéric Hecht
    • 2
  • Yvon Maday
    • 2
  1. 1.Mathematics and Computer Science DivisionArgonne National LaboratoryUSA
  2. 2.Laboratoire Jacques Louis LionsUniversité Pierre et Marie CurieParis cedex 05France

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