Daniele A. Di Pietro has been a Full Professor since 2012 and Deputy Director of Institut Montpelliérain Alexander Grothendieck at the University of Montpellier (France) since 2019. He is the author of two research monographs published by Springer and more than 80 scientific papers in refereed international journals or conference proceedings. His research fields include the development and analysis of advanced numerical methods for partial differential equations, with applications to fluid and solid mechanics and porous media. Over the course of his career, he has supervised ten PhD students and six postdoctoral fellows.

Jérôme Droniou was a Full Professor in France before moving to Monash university (Australia), where he has been an Associate Professor in the School of Mathematics since 2018, and head of the applied and computational section since 2019. He has authored two research monographs and more than 80 peer-reviewed articles and conference proceedings on theoretical and numerical analysis of partial differential equations. His current research interests revolve around the development of numerical methods for complex applications, and the design of mathematical tools to analyse the convergence of these methods. He has supervised a dozen PhD students and postdoctoral fellows in France and Australia.

Understanding the mathematical foundations helps the reader design methods for new applications

Bridging the gap between finite volumes, finite elements, and discontinuous Galerkin methods provides new insight on numerical methods

The mathematical setting for the continuous model is a key to successful approximation methods

Includes supplementary material: [...]

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