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, eBook

Reihe: Advances in Numerical Mathematics

the so called standard superconvergent div 6 PREFACE Contents 1 Basics 15 1.1 Meshes and shape functions ... ... .... ... .... .... ... ... 15 1.2 Spaces and approximation .... ... .... ... .... .... ... ... 19 2 Linear Diffusion I 33 3 Linear Diffusion II 67 4 Stokes Equations 89 8 CONTENTS 5 Flow Problems 105 5.1 Advection-Diffusion-ReactionEquation .. .... .... ... .... ... . 107 5.2 Oseen Equations .... ... .... ... .... .... ... .... ... . 110 5.3 Navier-Stokes Equations ... .... ... .... .... ... .... ... . 112 6 Linear Solvers 131 6.1 Krylov space methods . . . . . .... ... .... .... ... .... ... . 132 6.2 Interior Penalty . .... ... .... ... .... .... ... .... ... . 134 6.3 Local multigrid . .... ... .... ... .... .... ... .... ... . 145 6.4 LDG .... ... .... ... .... ... .... .... ... .... ... . 151 6.5 Advection Diffusion .. ... .... ... .... .... ... .... ... . 158 6.6 Stokes ... ... .... ... .... ... .... .... ... .... ... . 160 6.7 Oseen equations . .... ... .... ... .... .... ... .... ... . 162 A Example problems 167 A.1 Meshes and domains .. ... .... ... .... .... ... .... ... . 167 A.2 Poisson equation .... ... .... ... .... .... ... .... ... . 170 A.3 Advection-diffusion-reaction . .... ... .... .... ... .... ... . 171 A.4 Stokes and Oseen equations .. .... ... .... .... ... .... ... . 172 List of Figures 1.1 The set and (if ). . ... .... ... .... .... ... ... 17 1.2 The cel (dark grey) and the neighbor set (grey). Note that a common corner does not result in neighborhood. . . . . .... ... .... .... ... ... 19 2.1 Smallest eigenvalue of on a mesh of squares . .... .... ... ... 38 2.2 Eigenfunction to the smallest eigenvalue of for (left) and (right) on a mesh of squares . . . . . .... ... .... .... ... ... 39 2.3 Accuracy of the interior penalty method depending on the parameter . . ... 44 2.4 Pointwise errors on irregular meshes . . .... ... .... .... ... ... 55 2.5 Adapted mesh (level ) for the point value computation .... ... ... 60 2.6 -error over number of degrees of freedom for CG- , DG- and - elements (left) and (bi-)quadratic elements (right) .. .... .... ... ... 62

Zielgruppe

Research

Autoren/Hrsg.

Kanschat, Guido

Inhaltsverzeichnis

Linear Diffusion

Stokes Equations

Flow Problems

Linear Solvers

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

Über Autor(innen)

Dr. Guido Kanschat ist Assistant Professor an der Texas A & M University.