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### Mixed finite elements for global tide models with nonlinear damping

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 Title: Mixed finite elements for global tide models with nonlinear damping Authors: Cotter, CJGraber, PJKirby, RC Item Type: Journal 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. \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. Issue Date: 1-Dec-2018 Date of Acceptance: 19-Jun-2018 URI: http://hdl.handle.net/10044/1/61679 DOI: 10.1007/s00211-018-0980-4 ISSN: 0029-599X Publisher: Springer Verlag Start Page: 963 End Page: 991 Journal / Book Title: Numerische Mathematik Volume: 140 Issue: 4 Copyright Statement: © Springer-Verlag GmbH Germany, part of Springer Nature 2018. The final publication is available at Springer via https://link.springer.com/article/10.1007%2Fs00211-018-0980-4 Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)Engineering & Physical Science Research Council (EPSRC) Funder's Grant Number: EP/L000407/1EP/R029423/1 Keywords: Science & TechnologyPhysical SciencesMathematics, AppliedMathematicsSHALLOW-WATER EQUATIONSEXTERIOR CALCULUSWAVE-EQUATIONOCEANAPPROXIMATIONSOSCILLATIONSGALERKINmath.NAmath.NA65M12, 65M60, 35Q86math.NAmath.NA65M12, 65M60, 35Q860101 Pure Mathematics0102 Applied Mathematics0103 Numerical and Computational MathematicsNumerical & Computational Mathematics Publication Status: Published Online Publication Date: 2018-07-13 Appears in Collections: Applied Mathematics and Mathematical PhysicsFaculty of Natural SciencesMathematics