5 citations · 6 across the 5 of their papers we have counts for
9 papers
Space-time waveform relaxation multigrid for Navier-Stokes
James Jackaman, Scott MacLachlan
Space-time finite-element discretizations are well-developed in many areas of science and engineering, but much work remains within the development of specialized solvers for the r…
Predictions Based on Pixel Data: Insights from PDEs and Finite Differences
Elena Celledoni, James Jackaman, Davide Murari +1
As supported by abundant experimental evidence, neural networks are state-of-the-art for many approximation tasks in high-dimensional spaces. Still, there is a lack of a rigorous t…
Constraint-satisfying Krylov solvers for structure-preserving discretisations
James Jackaman, Scott MacLachlan
A key consideration in the development of numerical schemes for time-dependent partial differential equations (PDEs) is the ability to preserve certain properties of the continuum…
Invariant Variational Schemes for Ordinary Differential Equations
Alex Bihlo, James Jackaman, Francis Valiquette
We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variat…
Discrete conservation laws for finite element discretisations of multisymplectic PDEs
Elena Celledoni, James Jackaman
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is ob…
On the development of symmetry-preserving finite element schemes for ordinary differential equations
Alex Bihlo, James Jackaman, Francis Valiquette
In this paper we introduce a procedure, based on the method of equivariant moving frames, for formulating continuous Galerkin finite element schemes that preserve the Lie point sym…