The concept of multiresolution-based adaptive DG schemes for nonlinear one-dimensional hyperbolic conservation laws has been developed and investigated analytically and numerically in N. Hovhannisyan, S. Müller, R. Schäfer, Adaptive multiresolution Discontinuous Galerkin Schemes for Conservation Laws, Math. Comp., 2013. The key idea is to perform a multiresolution analysis using multiwavelets o...

We are concerned with the convergence of Lax-Wendroo type schemes with high resolution to the entropy solutions for conservation laws. These schemes include the original Lax-Wendroo scheme proposed by Lax and Wendroo in 1960 and its two step versions{the Richtmyer scheme and the MacCormack scheme. For the convex scalar conservation laws with algebraic growth ux functions, we prove the convergen...

We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau’s relative entropy method it turns out that in case of more than one conservation laws, in order that the system exhibit hydrodynamic behaviour, some particular identities reminiscent of Onsager’s recipro...

In this paper we study the asymptotic equivalence of a general system of 1-D conservation laws and the corresponding relaxation model proposed by S. Jin and Z. Xin (1995, Comm. Pure Appl. Math. 48, 235 277) in the limit of small relaxation rate. It is shown that if the relaxation system satisfies the subcharacteristic condition and the solution of the hyperbolic conservation laws is piecewise s...

The DFLU numerical flux was introduced in order to solve hyperbolic scalar conservation laws with a flux function discontinuous in space. We show how this flux can be used to solve systems of conservation laws. The obtained numerical flux is very close to a Godunov flux. As an example we consider a system modeling polymer flooding in oil reservoir engineering. Key-words: Finite volumes, finite ...

A mathematical formulation of conservation and of balance laws with random input data, specifically with random initial conditions, random source terms and random flux functions, is reviewed. The concept of random entropy solution is specified. For scalar conservation laws in multi-dimensions, recent results on the existence and on the uniqueness of random entropy solutions with finite variance...

A mathematical formulation of conservation and of balance laws with random input data, specifically with random initial conditions, random source terms and random flux functions, is reviewed. The concept of random entropy solution is specified. For scalar conservation laws in multi-dimensions, recent results on the existence and on the uniqueness of random entropy solutions with finite variance...