Preface
By writing this monograph. I would like first to provide a useful gathering of some knowledge that everybody involved in the numerical simulation of hyperbolic conservation laws could have learned in journals, in conferences communications, or simply by discussing with researchers or engineers. Most of the notions discussed along the chapters are indeed either extracted from journal articles, or are natural extensions of basic ideas introduced in these articles. At the moment I write this book, it seems that the materials concerning the subject of this book, the nonlinear stability of finite volume methods for hyperbolic systems of conservation laws, have never been put together and detailed systematically in unified notation. Indeed only the scalar case is fully developed in the existing textbooks. For this reason, I shall intentionally and systematically skip the notions that are almost restricted to scalar equations, like total variation bounds, or monotonicity properties. The most well-known system is the system of gas dynamics, and the examples I consider are all of gas dynamics type.