Publications

Space-time waveform relaxation multigrid for Navier-Stokes

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

Open Paper

Predictions based on pixel data: Insights from PDEs and finite differences

Journal of Computational Physics, 2025

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

Open Paper

Constraint-satisfying Krylov solvers for structure-preserving discretisations

SIAM Journal on Matrix Analysis and Applications, 2024

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

Open Paper

Invariant variational schemes for ordinary differential equations

Journal of Computational Physics, 2021

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.

Open Paper

Discrete conservation laws for finite element discretisations of multisymplectic PDEs

Journal of Computational Physics, 2021

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

Open Paper

Conservative Galerkin methods for dispersive Hamiltonian problems

CALCOLO, 2021

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

Open Paper

On the development of symmetry preserving finite element schemes for ordinary differential equations

Journal of Computational Dynamics, 2020

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.

Open Paper

The design of conservative finite element discretisations for the vectorial modified KdV equation

Applied Numerical Mathematics, 2019

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

Open Paper

Improving regional weather forecasts with neural interpolation

International Conference on Scientific Computing and Machine Learning, 2025

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

Open Paper

Quasinorms in semilinear elliptic problems

Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018, 2020

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

Open Paper

Finite element methods as geometric structure preserving algorithms

PhD thesis, University of Reading, 2018

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

Open Paper