ENGLISH

Mathematical Aspects of Discontinuous Galerkin Methods

By Daniele Antonio Di Pietro , Alexandre Ern (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2012
ISBN
9783642229794, 3642229794
DOI
10.1007/978-3-642-22980-0
Language
english
Format
PDF
Filesize
3 MB (2911905 bytes)
Series
Mathématiques et Applications 69
Edition
1
Pages
384\391
Library
Kolxo3
Time added
2012-08-21 20:00:00
Numerical Analysis; Computational Mathematics and

Description

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.

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