Daniel Appelö: Lagom Order Accurate Methods for Propagation of Waves in Deterministic and Stochastic Problems

In the first part of this talk we develop and analyze a new strategy for the spatial discontinuous Galerkin discretization of wave equations in second order form. The method features a direct, penalty and parameter-free approach to defining interelement fluxes. Both energy conserving and upwind discretizations can be devised. In the second part of this talk we discuss a new Multi-Order Monte Carlo method that uses our energy-DG method to quantify parametric uncertainties in scalar and elastic wave equations. Finally, time permitting, we suggest three new ideas for taming the CFL number of DG / spectral methods that allows for the tilmestep to be chosen independent of the order of the spatial discretization.