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Numerische Mathematik

, Volume 140, Issue 4, pp 963–991 | Cite as

Mixed finite elements for global tide models with nonlinear damping

  • Colin J. Cotter
  • P. Jameson Graber
  • Robert C. Kirby
Article

Abstract

We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy accumulation. We also give rates of damping in unforced systems and various continuous dependence results on initial conditions and forcing terms. A priori error estimates for the momentum and free surface elevation are given in \(L^2\) as well as for the time derivative and divergence of the momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.

Mathematics Subject Classification

65M12 65M60 35Q86 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Colin J. Cotter
    • 1
  • P. Jameson Graber
    • 2
  • Robert C. Kirby
    • 2
  1. 1.Imperial College LondonLondonUK
  2. 2.Department of MathematicsBaylor UniversityWacoUSA

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