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Project

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) (R-9719)

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.
Date:11 Mar 2019 →  14 Mar 2019
Keywords:evolution equations, Hybridized discontinuous Galerkin, Multiderivative methods
Disciplines:Applied mathematics in specific fields not elsewhere classified