In this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilizat...

It is well known that for a mixed initial-boundary hyberbolic system to be well-defined it is necessary to impose additional boundary conditions only on the inflow eigenspace of the problem. We prove the discrete analogue of the above concerning difference approximations to such a system; that is, imposing numerical boundary conditions which are at least zeroth-order accurate with an inflow par...

We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at optical frequency or an ideal negative metamaterial. We highlight an unusual instability phenomenon for this problem when the interface between the two media presents a rounded corner. To establish this result, we provi...

Our goal is to represent images in terms of geometric objects acting as primitive elements of an image description. Similar representations obtained by stochastic marked point processes have already led to convincing image analysis results but suffer from serious drawbacks such as complex and unstable parameter tuning, large computing time, and lack of generality. We propose an alternative desc...