  The dynamic Laplace operator arises from extending problems of isoperimetry
from fixed manifolds to manifolds evolved by general nonlinear dynamics.
Eigenfunctions of this operator are used to identify and track finite-time
coherent sets, which physically manifest in fluid flows as jets, vortices, and
more complicated structures. Two robust and efficient finite-element
discretisation schemes for numerically computing the dynamic Laplacian were
proposed in Froyland & Junge (2018). In this work we consider higher-order
versions of these two numerical schemes and analyse them experimentally. We
also prove the numerically computed eigenvalues and eigenvectors converge to
the true objects for both schemes under certain assumptions. We provide an
efficient implementation of the higher-order element schemes in an accompanying
Julia package.
