My current active research topics include: finite element discretisations for smectic liquid crystals, structure-preserving machine learning and geometric discretisations of flexible structures. If these sounds interesting/relevant to your work please feel free to contact me, I'm always happy to discuss maths.
James Jackaman and Scott MacLachlan, Preconditioned Krylov solvers for structure-preserving discretisations (in review), 2022.
Alex Bihlo, James Jackaman, and Francis Valiquette. Invariant variational schemes for ordinary differential equations. Stud. Appl. Math. (accepted), 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.