Jay Gopalakrishnan, University of Florida

KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

May 7-8, 2011

King Abdullah University of Science and Technology (KAUST)

Thuwal, Kingdom of Saudi Arabia

Designing New Discontinuous Petrov-Galerkin (DPG) Schemes

Petrov-Galerkin methods seek approximate solutions of boundary value problems in a "trial" space by weakly imposing the equations on a "test" space. A basic design principle is that while trial spaces must have good approximation properties, the test space must be chosen for stability. When this idea is applied to ultra-weak variational formulations, we obtain methods that exhibit remarkable stability properties. We will illustrate the idea using a simple transport equation as an example and proceed to generalize to more complex problems.