E-Book, Englisch, 180 Seiten
Kanschat Discontinuous Galerkin Methods for Viscous Incompressible Flow
2008
ISBN: 978-3-8350-5519-3
Verlag: Deutscher Universitätsverlag
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 180 Seiten
Reihe: Advances in Numerical Mathematics
ISBN: 978-3-8350-5519-3
Verlag: Deutscher Universitätsverlag
Format: PDF
Kopierschutz: 1 - PDF Watermark
The author reviews several discontinuous Galerkin schemes for elliptic and viscous flow problems. Setting out from Nitsche's method for weak boundary conditions, he studies the interior penalty and LDG methods. Combined with a stable advection discretization, they yield stable DG methods for linear flow problems of Stokes and Oseen type which are applied to the Navier-Stokes problem. The author not only presents the analytical techniques used to study these methods but also devotes a major discussion to the efficient numerical solution of discrete problems.
Dr. Guido Kanschat ist Assistant Professor an der Texas A & M University.
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;6
2;Contents;8
3;List of Figures;10
4;List of Tables;12
5;Chapter 1 Basics;15
5.1;1.1 Meshes and shape functions;15
5.2;1.2 Spaces and approximation;19
5.3;1.4 Advection Problems;27
6;Chapter 2 Linear Diffusion I;33
6.1;2.1 Weak boundary conditions;34
6.2;2.2 The Interior Penalty Method;36
6.3;2.3 Local error estimates;43
6.4;2.4 A posteriori error analysis;56
7;Chapter 3 Linear Diffusion II;66
7.1;3.1 The LDG Method;67
7.2;3.2 The standard LDG method;69
7.3;3.3 The “superconvergent” LDG method;76
8;Chapter 4 Stokes Equations;87
8.1;4.1 LDG discretization;89
8.2;4.2 Stable Finite Element Pairs;98
9;Chapter 5 Flow Problems;102
9.1;5.1 Advection-Diffusion-Reaction Equation;104
9.2;5.2 Oseen Equations;107
9.3;5.3 Navier-Stokes Equations;109
10;Chapter 6 Linear Solvers;128
10.1;6.1 Krylov space methods;129
10.2;6.2 Interior Penalty;131
10.3;6.3 Local multigrid;142
10.4;6.4 LDG;148
10.5;6.5 Advection Diffusion;155
10.6;6.6 Stokes;157
10.7;6.7 Oseen equations;159
11;Appendix A Example problems;164
11.1;A.1 Meshes and domains;164
11.2;A.2 Poisson equation;167
11.3;A.3 Advection-diffusion-reaction;168
11.4;A.4 Stokes and Oseen equations;169
12;Bibliography;172
13;Index;178
