Applied Mathematics Seminar

In the western Pacific ocean, two dynamically active layers have been identified---to model their evolution we suppose the interaction between the layers is weak. The same trick works generally to form numerical discretisations: we cut the domain into finite sized elements by initially artificially insulating them from each other; then centre manifold theory is applied to generate a discretisation that incorporates the actual coupling between the elements. There are manyfold benefits: it gives new theoretical support for use of the discretisation at finite element size; in practice this comes from resolving subgrid scale structures and interactions between physical processes; which generally improves stability properties of the discretisation; a model can be systematically refined; boundary conditions are easily incorporated; novel features of initial conditions are derived to ensure long term accuracy; the same modelling paradigm is used for both numerical and analytic models.