Mixed finite elements for global tide models with nonlinear damping
File(s)
Accepted version
Author(s)
Cotter, Colin J
Graber, P Jameson
Kirby, Robert C
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.
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.
Date Issued
2018-12-01
Date Acceptance
2018-06-19
Citation
Numerische Mathematik, 2018, 140 (4), pp.963-991
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
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://arxiv.org/abs/1706.01352v1
Grant Number
EP/L000407/1
EP/R029423/1
Subjects
math.NA
math.NA
65M12, 65M60, 35Q86
Publication Status
Published
Date Publish Online
2018-07-13