126 citations · 181 across the 14 of their papers we have counts for
14 papers
On discrete analogues of potential vorticity for variational shallow water systems
Elizabeth L. Mansfield
We outline how discrete analogues of the conservation of potential vorticity may be achieved in Finite Element numerical schemes for a variational system which has the particle rel…
On Poisson structures arising from a Lie group action
G. M. Beffa, E. L. Mansfield
We investigate some infinite dimensional Lie algebras and their associated Poisson structures which arise from a Lie group action on a manifold. If is a Lie group, $\g$ its Lie…
On the use of the Rotation Minimising Frame for Variational Systems with Euclidean Symmetry
E. L. Mansfield, A. Rojo-Echeburua
We study variational systems for space curves, for which the Lagrangian or action principle has a Euclidean symmetry, using the Rotation Minimising frame, also known as the Normal,…
Moving Frames and Noether's Conservation Laws - the General Case
Tânia M. N. Gonçalves, Elizabeth L. Mansfield
In recent works, the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Usi…
Discrete moving frames and discrete integrable systems
Elizabeth Mansfield, Gloria Marí Beffa, Jing Ping Wang
Group based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. H…
Noether type discrete conserved quantities arising from a finite element approximation of a variational problem
Elizabeth Mansfield, Tristan Pryer
In this work we prove a weak Noether type theorem for a class of variational problems which include broken extremals. We then use this result to prove discrete Noether type conserv…