Abstract
When dealing with hyperbolic systems of conservation laws, popular methods, like finite volumes, WENO or DG method use a discontinuous approximation of data. The rational is that, since the solutions we are looking for are a priori discontinuous, it is safer to look for discontinuous approximations.
Concerning continuous approximation a potential candidate, among others, is the SUPG method, or the stream line diffusion method. However it is often said that such methods are not locally conservative.
In this talk I will show/explain that:
1- one can construct a class of methods, using a globally continuous approximation of data, that are able to compute very good approximations,
2- This type of approximation, and the continuous finite element methods (with artificial viscosity) are locally conservative: one can exhibit flux.
3- There is a systematic procedure that can make them entropy stable, and then one can control the amount of dissipation,
4- They can be arbitrary high order, with the same stencil as discontinuous Galerkin methods
This is a joint work with M. Ricchiuto (Inria, France), P. Bacigaluppi (Zurich) and S. Tokareva (Los Alamos)