Discontinuous Galerkin Method: Analysis and Applications to Compressible Flow

✍ Scribed by Vít Dolejší, Miloslav Feistauer (auth.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 575
• Series: Springer Series in Computational Mathematics 48
• Edition: 1
• Category: Library

✦ Synopsis

The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.

✦ Table of Contents

Front Matter....Pages i-xiv
Introduction....Pages 1-23
Front Matter....Pages 25-25
DGM for Elliptic Problems....Pages 27-84
Methods Based on a Mixed Formulation....Pages 85-115
DGM for Convection-Diffusion Problems....Pages 117-169
Space-Time Discretization by Multistep Methods....Pages 171-222
Space-Time Discontinuous Galerkin Method....Pages 223-335
Generalization of the DGM....Pages 337-397
Front Matter....Pages 399-399
Inviscid Compressible Flow....Pages 401-475
Viscous Compressible Flow....Pages 477-519
Fluid-Structure Interaction....Pages 521-551
Back Matter....Pages 553-572

✦ Subjects

Numerical Analysis; Computational Science and Engineering; Mathematical Modeling and Industrial Mathematics; Applications of Mathematics