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 …

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 …

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 …

We study the entropy stability of difference approximations to nonlinear hyperbolic
conservation laws, and related time-dependent problems governed by additional dissipative …

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 …

Abstract Current models on Explainable Artificial Intelligence (XAI) have shown a lack of
reliability when evaluating feature-relevance for deep neural biomarker classifiers. The …

Sympathetic cooling of two atomic isotopes is experimentally investigated. Using forced
evaporation of a bosonic 7 Li gas in a magnetic trap, a sample of 1.3× 10 5 6 Li fermions has …

The method of compensated compactness as a technique for studying hyperbolic
conservation laws is of fundamental importance in many branches of applied mathematics …

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 …