|Date:||Tue, May 24, 2011|
|Place:||IRC East Wing Seminar Room|
Abstract: In this talk, we will discuss our ongoing work to develop a new adaptive scheme to solve first order transport equation. In this problem, solutions typically exhibit strong anisotropic features such as shear layers. First, we introduce stable variational formulation which allows us to choose L2 as a space, in which the variational solution is sought. This will provide a flexible variational framework where one could use L2 directional frames such as curvelets and shearlets to effectively resolve anisotropic features of the solution. Secondly, we discuss directional representation system which can be potentially used in the context of PDE.