FoCM 2014 conference
Workshop C2 - Foundation of Numerical PDE's
December 19, 15:10 ~ 15:45 - Room A22
Norms in the analysis of the DPG method with optimal test functions
Norbert Heuer
Pontificia Universidad Catolica de Chile, Chile - nheuer@mat.puc.cl
Standard analysis of the discontinuous Petrov-Galerkin method (DPG) with optimal test functions is based on a direct relationship between trial and test spaces, and their norms. Depending on the particular problem under consideration, theoretical and practical requirements imply different conditions both for the selection of spaces and for the definition of norms. In this talk, we discuss several cases (like convection-dominated diffusion, non-conforming trace approximation, and hypersingular boundary integral operators) and show how problem-dependent objectives force the selection of norms
Joint work with Leszek Demkowicz (The University of Texas at Austin, USA), Michael Karkulik (Pontificia Universidad Catolica de Chile) and Francisco-Javier Sayas (University of Delaware, USA).