Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
SIAM Journal on Scientific Computing
Finite-volume transport on various cubed-sphere grids
Journal of Computational Physics
Numerical wave propagation on the hexagonal C-grid
Journal of Computational Physics
SIAM Journal on Scientific Computing
Numerical representation of geostrophic modes on arbitrarily structured C-grids
Journal of Computational Physics
Rehabilitation of the Lowest-Order Raviart-Thomas Element on Quadrilateral Grids
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Efficient Assembly of $H(\mathrm{div})$ and $H(\mathrm{curl})$ Conforming Finite Elements
SIAM Journal on Scientific Computing
Inspection of hexagonal and triangular C-grid discretizations of the shallow water equations
Journal of Computational Physics
Mixed finite elements for numerical weather prediction
Journal of Computational Physics
Hi-index | 31.45 |
We describe discretisations of the shallow-water equations on the sphere using the framework of finite element exterior calculus, which are extensions of the mimetic finite difference framework presented in Ringler (2010) [11]. The exterior calculus notation provides a guide to which finite element spaces should be used for which physical variables, and unifies a number of desirable properties. We present two formulations: a ''primal'' formulation in which the finite element spaces are defined on a single mesh, and a ''primal-dual'' formulation in which finite element spaces on a dual mesh are also used. Both formulations have velocity and layer depth as prognostic variables, but the exterior calculus framework leads to a conserved diagnostic potential vorticity. In both formulations we show how to construct discretisations that have mass-consistent (constant potential vorticity stays constant), stable and oscillation-free potential vorticity advection.