The DPG Method for Convection-Reaction Problems

We present a progress report on the development of Discontinuous Petrov-Galerkin methods for the convection-reaction problem in context of time-stepping and space-time discretizations of Boltzmann equations [1].
The work includes a complete analysis for both conforming (DPGc) and non-nonconforming (DPGd) versions of the DPG method employing either globally continuous or discontinuous piece-wise polynomials to discretize the traces.
The results include construction of a local Fortin operator for the case of constant convection and a global discrete stability analysis for both DPGc and DPGd methods.
The theoretical findings are illustrated with numerous numerical experiments in two space dimensions.

This is a joint work with Nathan Roberts from Sandia National Laboratories.

Slides (PDF)

[1] L. Demkowicz, N. Roberts, "The DPG Method for the Convection–Reaction Problem Revisited", submitted.