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@article{Shipton:2018:10.1016/j.jcp.2018.08.027,
author = {Shipton, J and Gibson, TH and Cotter, CJ},
doi = {10.1016/j.jcp.2018.08.027},
journal = {Journal of Computational Physics},
pages = {1121--1137},
title = {Higher-order compatible finite element schemes for the nonlinear  rotating shallow water equations on the sphere},
url = {http://dx.doi.org/10.1016/j.jcp.2018.08.027},
volume = {375},
year = {2018}
}

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TY  - JOUR
AB  - We describe a compatible finite element discretisation for the shallow waterequations on the rotating sphere, concentrating on integrating consistentupwind stabilisation into the framework. Although the prognostic variables are velocity and layer depth, the discretisation has a diagnostic potentialvorticity that satisfies a stable upwinded advection equation through aTaylor-Galerkin scheme; this provides a mechanism for dissipating enstrophy at the gridscale whilst retaining optimal order consistency. We also use upwind discontinuous Galerkin schemes for the transport of layer depth. These transport schemes are incorporated into a semi-implicit formulation that is facilitated by a hybridisation method for solving the resulting mixed Helmholtz equation. We illustrate our discretisation with some standard rotating sphere test problems.
AU  - Shipton,J
AU  - Gibson,TH
AU  - Cotter,CJ
DO  - 10.1016/j.jcp.2018.08.027
EP  - 1137
PY  - 2018///
SN  - 0021-9991
SP  - 1121
TI  - Higher-order compatible finite element schemes for the nonlinear  rotating shallow water equations on the sphere
T2  - Journal of Computational Physics
UR  - http://dx.doi.org/10.1016/j.jcp.2018.08.027
UR  - http://arxiv.org/abs/1707.00855v1
UR  - http://hdl.handle.net/10044/1/63551
VL  - 375
ER  -

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