525 citations · 882 across the 9 of their papers we have counts for
6 papers · 1 filter
The scaling and skewness of optimally transported meshes on the sphere
Chris J. Budd, Andrew T. T. McRae, Colin J. Cotter
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of intere…
Optimal-transport-based mesh adaptivity on the plane and sphere using finite elements
Andrew T. T. McRae, Colin J. Cotter, Chris J. Budd
In moving mesh methods, the underlying mesh is dynamically adapted without changing the connectivity of the mesh. We specifically consider the generation of meshes which are adapte…
Automated generation and symbolic manipulation of tensor product finite elements
Andrew T. T. McRae, Gheorghe-Teodor Bercea, Lawrence Mitchell +2
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilater…
On the shallow atmosphere approximation in finite element dynamical cores
C. J. Cotter, D. A. Ham, A. T. T. McRae +2
We provide an approach to implementing the shallow atmosphere approximation in three dimensional finite element discretisations for dynamical cores. The approach makes use of the f…
Compatible finite element methods for numerical weather prediction
C. J. Cotter, A. T. T. McRae
This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid st…
Energy- and enstrophy-conserving schemes for the shallow-water equations, based on mimetic finite elements
Andrew T. T. McRae, Colin J. Cotter
This paper presents a family of spatial discretisations of the nonlinear rotating shallow-water equations that conserve both energy and potential enstrophy. These are based on two-…