DPG for Convective Problems I
Dr. Clemens HofreitherDec. 15, 2009, 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 ﬁrst seminar talk, we present the abstract framework underlying the class of methods presented in the above article. Speciﬁcally, we introduce the idea of optimal test functions which are computed on the ﬂy to yield optimal stability for a speciﬁc variational formulation. Spaces of discontinuous functions are employed in order to be able to approximate the optimal test functions locally and cheaply. We then give as a simple example a purely convective problem in 1D. In this setting, optimal test functions can be analytically computed.