Mathematical Aspects of Discontinuous Galerkin Methods [electronic resource] /
Di Pietro, Daniele Antonio.author.
Ern, Alexandre.author.
This book introduces the basic ideas for building discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. It 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 utilized 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.
Description based upon print version of record.
Includes bibliographical references and indexes.
Basic concepts -- Steady advection-reaction -- Unsteady first-order PDEs -- PDEs with diffusion -- Additional topics on pure diffusion -- Incompressible flows -- Friedhrichs' Systems -- Implementation.
This book introduces the basic ideas for building discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. It 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 utilized 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.
Numerical analysis.
Computer mathematics.
Applied mathematics.
Engineering mathematics.
Numerical Analysis.
Computational Mathematics and Numerical Analysis.
Mathematical and Computational Engineering.

Mathématiques et Applications