Mathematical Aspects of Discontinuous Galerkin Methods

From the reviews: "The goal of this book is to provide graduate students and researchers in numerical methods with the basic mathematical concepts to design and analyze discontinuous Galerkin (DG) methods for various model problems, starting at an introductory level and further elaborating on more advanced topics, considering that DG methods have tremendously developed in the last decade." (Remi Vaillancourt, Mathematical Reviews, January, 2013) "The book is structured in three parts: scalar first order PDEs, scalar second order PDEs, and systems. ... For researchers in numerical analysis it is nice to see that for all problem classes the authors start with a full analysis of existence, uniqueness, and properties of the solution of the continuous problem. ... this new monograph is an extremely valuable source concerning the theoretical function of dG methods for the advanced reader." (H.-G. Roos, SIAM Review, Vol. 55 (2), 2013) "This new monograph is an extremely valuable collection of the mathematical treatment of discontinuous Galerkin methods with 300 references and providing profound insight into the required techniques. It collects and presents also several recent results for elliptic and non-elliptic, stationary and non-stationary partial differential equations in a unified framework. Thus it is strongly recommendable for researchers in the field." (Christian Wieners, Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 92 (7), 2012) "The aim of the book is 'to provide the reader with the basic mathematical concepts to design and analyze discontinuous Galerkin methods for various model problems, starting at an introductory level and further elaborating on more advanced topics'. ... Some useful practical implementation aspects are considered in an Appendix. The bibliography contains more than 300 entries." (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol. 1231, 2012)

• Basic concepts.- Steady advection-reaction.- Unsteady first-order PDEs.- PDEs with diffusion.- Additional topics on pure diffusion.- Incompressible flows.- Friedhrichs' Systems.- Implementation.