Error Estimates for Well-Balanced Schemes on Simple Balance Laws

• 1 Introduction.- 2 Local and global error estimates.- 3 Position-dependent scalar balance laws.- 4 Lyapunov functional for inertial approximations.- 5 Entropy dissipation and comparison with Lyapunov estimates.- 6 Conclusion and outlook.

"The main purpose of the book is to present an analysis of global (in space) error bounds for well-balanced schemes with a specific emphasis on the time dependence of such bounds. ... The book will be of interest to anyone willing to design and/or study well-balanced schemes, either from an analytical or practical point of view. ... this book will surely contribute to future improvements in the field." (Jean-Francois Coulombel, Mathematical Reviews, August, 2016) "All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements. Each chapter is more or less self-containing, it has its own abstract, introduction and the list of references." (Vit Dolejsi, zbMATH 1332.65132, 2016)