Research

Active research topics:

• Coupling neural networks into finite element models

• Structure preserving finite element methods

• Smectic liquid crystals

• Accelerating linear solvers

If these sounds interesting/relevant to your work please feel free to contact me, I'm always happy to discuss maths.

Publications

• James Jackaman and Oliver Sutton, Improving regional weather forecasts with neural interpolation, International Conference on Scientific Computing and Machine Learning, 2025.

• Elena Celledoni, James Jackaman, Davide Murari and Brynjulf Owren, Predictions based on pixel data: Insights from PDEs and finite differences (accepted), 2025.

• James Jackaman and Scott MacLachlan, Space-time waveform relaxation multigrid for Navier-Stokes (in review), 2024.

• James Jackaman and Scott MacLachlan, Constraint-satisfying Krylov solvers for structure-preserving discretisations. SIMAX, 2024.

• Alex Bihlo, James Jackaman, and Francis Valiquette. Invariant variational schemes for ordinary differential equations. Stud. Appl. Math, 2021; 1 - 30.

• Elena Celledoni and James Jackaman. Discrete conservation laws for finite element discretisations of multisymplectic PDEs. Journal of Computational Physics, Volume 444, 2021, 110520.

• James Jackaman and Tristan Pryer. Conservative Galerkin methods for dispersive Hamiltonian problems. CALCOLO 58, 35 2021.

• Alex Bihlo, James Jackaman, and Francis Valiquette. On the development of symmetry preserving finite element schemes for ordinary differential equations. Journal of Computational Dynamics (accepted), 2020.

• James Jackaman and Tristan Pryer. Quasinorms in semilinear elliptic problems. Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018, Springer Verlag, 2020.

• James Jackaman, Georgios Papamikos, and Tristan Pryer. The design of conservative finite element discretisations for the vectorial modified KdV equation. Applied Numerical Mathematics, 137:230– 251, 2019.

Thesis

• PhD thesis: Finite element methods as structure preserving algorithms, 2019.