| Speaker: | Daniele Di Pietro, ENPC - CERMICS |
| Title: | Discontinuous Galerkin methods for anisotropic and locally vanishing diffusion with advection |
| Time: | 3:00-4:00 pm |
| Place: | Blocker 628 |
The development and analysis of Discontinuous Galerkin methods has up
to now followed two separate paths according to the hyperbolic or
elliptic nature of the problem at hand.
However, when considering advection-diffusion PDEs with locally
vanishing diffusion, the nature of the problem is not necessarily
uniform all over the domain.
To the knowledge of the authors, all the methods proposed for this
class of equations require the a priori individuation of the
elliptic-hyperbolic interface in order to tailor stabilization terms,
which is possibly a difficult task when working in finite precision
or when dealing with non-linear problems. In the present work we
construct and analyze a method which automatically detects such an
interface without requiring any further intervention.
To do so, we show the need to deploy weighted average and jump
boundary operators in consistency terms.
The proposed analysis framework provides optimal estimates in the
graph norm and allows to recover well-known results when the problem
is either entirely hyperbolic or uniformly elliptic.
Theoretical results are supported by numerical evidence.
Joint work with A. Ern and J.-L. Guermond.
Last revised: 10/09/06 By: christov@math