| 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