Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, January 28, 2013 - 08:00 to 09:00
Location: 
Kidder 364

Speaker Info

Institution: 
Portland State University
Abstract: 

Variational formulations of the Petrov-Galerkin type use different 'test' and 'trial' spaces. The solution is sought in a space of 'trial' functions, while the equations are imposed using a space of 'test' functions. A guiding principle in design of good methods is that the trial functions must have good approximation properties, while test functions should be chosen to obtain stability. The best test spaces in Petrov-Galerkin methods give the best stability constants. What are these optimal test spaces? Abstractly, the answer is easy to write down. However, designing practical methods using such optimal test spaces is an ongoing challenge. We report on the directions we have taken, in collaboration with L. Demkowicz, to construct new Discontinuous Petrov-Galerkin (DPG) methods, and in particular, on localizing the global problem of constructing optimal test spaces.