Research-High order method for systems of conservation laws using continuous approximation of data

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High order method for systems of conservation laws using continuous approximation of data

Speaker: Remi Abgrall (University of Zurich)
Time: Jun 5, 2019, 15:00-16:00
Location: Conference Room 415, Hui Yuan 3#

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)