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

Daniel Appelö
Department of Mathematics and Statistics
University of New Mexico
Albuquerque, New Mexico, USA


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.