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arXiv · 1706.01352

Mixed finite elements for global tide models with nonlinear damping

Colin J. Cotter·P. Jameson Graber·Robert C. Kirby
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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. \emph{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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Colin J. Cotter, P. Jameson Graber, Robert C. Kirby. 2017-06-05. Mixed finite elements for global tide models with nonlinear damping. https://arxiv.org/abs/1706.01352

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