Daniel Appelö
Department of Mathematics and Statistics
University of New Mexico
Albuquerque, New Mexico, USA
Starting from a kinetic and potential energy density 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, mesh-independent approach to defining interelement fluxes. Both energy- conserving and upwind discretizations can be devised. We derive a priori error estimates in the energy norm for certain fluxes and present numerical experiments showing that optimal convergence in L2 is obtained. We also show how the method can be applied to the scalar wave equation as well as the elastic wave equation.
The talk will be informal and I will start by explaining the main idea behind the method on the board for the scalar 1D wave equation $u_{tt} = c^2 u_{xx}$ with the energy density $u_t^2 / 2 + (c u_x)^2 / 2$.