Publisher Summary This chapter focuses on finite volume methods. The finite volume
method is a discretization method that is well suited for the numerical simulation of various …

Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlapping control volumes. Degrees of …

This book gives a general presentation of the mathematical and numerical connections
kinetic theory and conservation laws based on several earlier works with PL Lions and E …

ON A CELL ENTROPY INEQUALITY FOR DISCONTINUOUS GALERKIN METHODS (1.1) ut +
div f(u) = 0. Page 1 mathematics of computation volume 62, number 206 april 1994, pages …

The use of multiresolution decompositions in the context of finite volume schemes for
conservation laws was first proposed by A. Harten for the purpose of accelerating the …

One approximates the entropy weak solution u of a nonlinear parabolic degenerate
equation u_t+\rmdiv(\mathbfqf(u))-Δϕ(u)=0 by a piecewise constant function u_\mathcalD …

This paper is devoted to the study of an error estimate of the finite volume, approximation to
the solution u L∞(RN x R) of the equation ut+ div (V f (u))= 0, where v is a vector function …

We give a synthetic statement of Kružkov-type estimates for multi-dimensional scalar
conservation laws. We apply it to obtain various estimates for different approximation …

In this paper we shall derive a posteriori error estimates in the $ L^ 1$-norm for upwind finite
volume schemes for the discretization of nonlinear conservation laws on unstructured grids …

In this paper, we give a simple introduction to the devising of discontinuous Galerkin (DG)
methods for nonlinear hyperbolic conservation laws. These methods have recently made …