Daniele Antonio Di Pietro, Alexandre Ern

Mathematical Aspects of Discontinuous Galerkin Methods

• Broschiertes Buch

Produktbeschreibung

This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.

Produktdetails

• Mathématiques et Applications 69
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 80083576, 978-3-642-22979-4
• Seitenzahl: 404
• Erscheinungstermin: 4. November 2011
• Englisch
• Abmessung: 235mm x 155mm x 22mm
• Gewicht: 622g
• ISBN-13: 9783642229794
• ISBN-10: 3642229794
• Artikelnr.: 33692746

Autorenporträt

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.

Inhaltsangabe

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

Rezensionen

From the reviews: "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 für 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) "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." (Rémi Vaillancourt, Mathematical Reviews, January, 2013)