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Finite Volume Multilevel Approximation of the Shallow Water Equations

In: Partial Differential Equations: Theory, Control and Approximation

Author

Listed:
  • Arthur Bousquet

    (Indiana University, The Institute for Scientific Computing and Applied Mathematics)

  • Martine Marion

    (Indiana University, The Institute for Scientific Computing and Applied Mathematics
    Université de Lyon, Ecole Centrale de Lyon, CNRS UMR 5208, Département Mathématique Informatique)

  • Roger Temam

    (Indiana University, The Institute for Scientific Computing and Applied Mathematics)

Abstract

The authors consider a simple transport equation in one-dimensional space and the linearized shallow water equations in two-dimensional space, and describe and implement a multilevel finite-volume discretization in the context of the utilization of the incremental unknowns. The numerical stability of the method is proved in both cases.

Suggested Citation

  • Arthur Bousquet & Martine Marion & Roger Temam, 2014. "Finite Volume Multilevel Approximation of the Shallow Water Equations," Springer Books, in: Philippe G. Ciarlet & Tatsien Li & Yvon Maday (ed.), Partial Differential Equations: Theory, Control and Approximation, edition 127, pages 67-98, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-41401-5_3
    DOI: 10.1007/978-3-642-41401-5_3
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