# DPG for Convective Problems II

## Dipl.-Ing. Michael Kolmbauer

Jan. 12, 2010, 3:30 p.m. P 215

In this series of two seminar talks, we review the paper A Class of Discontinuous Petrov-Galerkin Methods. Part II: Optimal Test Functions by L. Demkowicz and J. Gopalakrishnan, available
online.

In this second seminar talk, we repeat the abstract framework underlying the class of DPG-methods presented in the above article once more.

Instead of the purely convective problem, we apply these ideas to a convection-dominated diﬀusion problem in 1D. We calculate the energy norm in the setting of a single-element approximation and study its equivalence to $L^2$-type norms. Therein we show, that the DPG method delivers $O(1)$ stability for the stress, $uniformly$ in the diﬀusion constant.