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Mixed finite elements for global tide models with nonlinear damping

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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.

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Authors and Affiliations

  1. Imperial College London, South Kensington Campus, London, SW7 2AZ, UK

    Colin J. Cotter

  2. Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX, 76798-7328, USA

    P. Jameson Graber & Robert C. Kirby

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  1. Colin J. Cotter
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  2. P. Jameson Graber
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  3. Robert C. Kirby
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Correspondence to Robert C. Kirby.

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Cotter, C.J., Graber, P.J. & Kirby, R.C. Mixed finite elements for global tide models with nonlinear damping. Numer. Math. 140, 963–991 (2018). https://doi.org/10.1007/s00211-018-0980-4

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  • DOI: https://doi.org/10.1007/s00211-018-0980-4

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