Developments in Multilevel Methods for Time Dependent Hyperbolic PDEs

Luke Olson

Department of Applied Mathematics
Campus Box 526
University of Colorado at Boulder
Boulder CO 80309-0526


Abstract

Many applications involve convection dominated flow and to this end we present an approach for efficiently solving the pure advection problem. Our discussion focuses on linear problems with discontinuous inflow boundary data and divergence-free flow fields, which arise in many time-dependent models. We analyze a non-conforming finite element discretization within a least-squares setting and discuss the solution of the algebraic system in a multi-level framework.