## Seminar in Numerical Analysis: Rémi Abgrall (Universität Zürich)

**Some recent results on the approximation of conservation laws: revisiting the notion of conservation**

Since the work of B. Wendroff and P. Lax, we know what should be the correct form of the numerical approximation of conservation law. We also know, after Hou and Le Floch, what kind of problems we are facing when the flux form is not respected.

However, this is not the end of the story. All these works use a one dimensional way of thinking: the main player is the normal flux across cell interfaces. In addition there are several excellent numerical methods that do not fit the form of the lax Wendroff theorem.

In that talk, I will introduce a more general setting and show that any reasonable scheme for conservation law can be put in that framework. In addition, I will show that an equivalent flux formulation, with a suitable definition of what is a flux, can be explicitly constructed (and computed), so that any reasonable scheme can be put in a finite volume form.

I will end the talk by showing some applications: how to systematically construct entropy stable scheme, or starting from the non conservative form of a system-say the Euler equations-, how to construct a suitable discretisation. And more.

This is a joint work with P. Bacigaluppi (now postdoc at ETH) and S. Tokareva (now at Los Alamos).

For further information about the seminar, please visit this webpage.

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