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
Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations
Journal of Computational Physics
Numerical wave propagation on the hexagonal C-grid
Journal of Computational Physics
Some remarks on quadrilateral mixed finite elements
Computers and Structures
Numerical representation of geostrophic modes on arbitrarily structured C-grids
Journal of Computational Physics
Journal of Computational Physics
Numerical wave propagation for the triangular P1DG-P2 finite element pair
Journal of Computational Physics
A finite element exterior calculus framework for the rotating shallow-water equations
Journal of Computational Physics
Hi-index | 31.45 |
We show how mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo-uniform grids. This family of mixed finite element methods can be thought of in the numerical weather prediction context as a generalisation of the popular polygonal C-grid finite difference methods. There are a few major advantages: the mixed finite element methods do not require an orthogonal grid, and they allow a degree of flexibility that can be exploited to ensure an appropriate ratio between the velocity and pressure degrees of freedom so as to avoid spurious mode branches in the numerical dispersion relation. These methods preserve several properties of the C-grid method when applied to linear barotropic wave propagation, namely: (a) energy conservation, (b) mass conservation, (c) no spurious pressure modes, and (d) steady geostrophic modes on the f-plane. We explain how these properties are preserved, and describe two examples that can be used on pseudo-uniform grids: the recently-developed modified RTk-Q(k-1) element pairs on quadrilaterals and the BDFM1-P1"D"G element pair on triangles. All of these mixed finite element methods have an exact 2:1 ratio of velocity degrees of freedom to pressure degrees of freedom. Finally we illustrate the properties with some numerical examples.