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, CJ
Graber, PJ
Kirby, 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: Dec-2018
Date of Acceptance: 19-Jun-2018
URI: http://hdl.handle.net/10044/1/61679
DOI: https://doi.org/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)
Funder's Grant Number: EP/L000407/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
SHALLOW-WATER EQUATIONS
EXTERIOR CALCULUS
WAVE-EQUATION
OCEAN
APPROXIMATIONS
OSCILLATIONS
GALERKIN
math.NA
math.NA
65M12, 65M60, 35Q86
math.NA
math.NA
65M12, 65M60, 35Q86
Numerical & Computational Mathematics
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0101 Pure Mathematics
Publication Status: Published
Online Publication Date: 2018-07-13
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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