The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

Weak and Measure-valued Solutions to Evolutionary PDEs Page 1 Weak and Measure-valued
Solutions to Evolutionary PDEs Page 2 APPLIED MATHEMATICS AND MATHEMATICAL …

This is the second edition of a well-received book providing the fundamentals of the theory
hyperbolic conservation laws. Several chapters have been rewritten, new material has been …

This paper attempts to give a qualitative and quantitative description of the numerical error
introduced by using finite difference schemes in nonconservative form for scalar …

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 …

We establish the convergence of the finite volume method applied to multidimensional
hyperbolic conservation laws and based on monotone numerical flux-functions. Our …

This paper investigates the convergence of the smooth solutions u; to the initial value
problem for a nonlinear diffusive–dispersive equation:@ tu+@ xf (u)=@ xÿ (@ xu)−@ 3 xu (x; …

In this paper, an ${L^\infty}({L^ 1}) $-error estimate for a class of finite volume methods for
the approximation of scalar multidimensional conservation laws is obtained. These methods …

Convergence and error estimates in finite volume schemes for general multidimensional scalar
conservation laws. I. Explicite mon Page 1 M2AN - MODÉLISATION MATHÉMATIQUE ET ANALYSE …

We introduce a technique that makes every explicit Runge--Kutta (ERK) time stepping
method invariant domain preserving and mass conservative when applied to high-order …