Discontinuous Galerkin Methods for Viscous Incompressible Flow (2008) (Advances in Numerical Mathematics)

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Synopsis
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
Copyright:
2008

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9783835055193
Related ISBNs:
9783835040014
Publisher:
Deutscher Universitätsverlag
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Copyrighted By:
N/A
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No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Mathematics and Statistics
Submitted By:
Bookshare Staff
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This is a copyrighted book.

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