Title
FWO travel grant for a short stay abroad in the United states of America (Houston): SIAM Conference on Mathematical & Computational Issues in the Geosciences (GS19) (Research)
Abstract
In this talk, we consider the numerical treatment of evolution equations of form w_t +
Q(w) = 0, where Q can of course be a differential operator. Convection-diffusion
equation, the Navier-Stokes equations and many more fall into this rather general
framework. Here, we focus on the discretization of the time-derivative using a multiderivative
approach. This means that, unlike in classical one-step methods, not only
Q(w) is taken into account, but also Q'(w) Q(w), which is the second-derivative of w.
For the equations we have in mind, we favour implicit methods to remove a (possibly
severe) CFL condition.
We discuss several possibilities of implementing implicit multiderivative solvers into
an existing HDG (hybridized discontinuous Galerkin) solver and show weaknesses
and strengths of the approaches. In particular, we show why a standard Cauchy-
Kovalewskaya-approach can fail, and we present a uniformly stable fix.
Period of project
11 March 2019 - 14 March 2019