Publications

We develop a new space-time solver for the Navier-Stokes equation.

We design a neural interpolation operator to improve the boundary data for regional weather models.

We aim to understand convolutional neural networks analytically through comparing them to finite difference methods.

We propose a modification to the standard flexible generalised minimum residual (FGMRES) iteration that enforces selected constraints on approximate numerical solutions.

We propose a new algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler–Lagrange equations of a variational principle.

In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation.

We design and analyse a discontinuous Galerkin scheme for a generalised KdV equation.

We examine the a priori and a posteriori analysis of discontinuous Galerkin finite element discretisations of semilinear elliptic PDEs with polynomial nonlinearity.

We introduce a procedure, based on the method of equivariant moving frames, for formulating continuous Galerkin finite element schemes that preserve the Lie point symmetries of initial value problems for ordinary differential equations.

We design the first consistent Galerkin scheme for the approximation of the vectorial modified Korteweg-de Vries equation.

Here we investigate finite element techniques aimed at preserving the underlying geometric structures for various problems, and, in doing so, develop new geometric structure preserving methods.