In many application domains, the preferred approaches to the numerical solution of hyperbolic partial differential equations such as conservation laws are formulated as finite difference schemes. While finite difference schemes are amenable to physical interpretation, one disadvantage of finite difference formulations is that it is relatively difficult to derive the so-called goal oriented a po...

L -error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L norm is of order h at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch’s theory which was originally developed ...

The Multiscale Finite-Volume (MSFV) method has been recently developed and tested for multiphase-flow problems with simplified physics (i.e. incompressible flow without gravity and capillary effects) and proved robust, accurate and efficient. However, applications to practical problems necessitate extensions that enable the method to deal with more complex processes. In this paper we present a ...