Moving finite elements:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon
1994
|
| Series: | Monographs on numerical analysis
Oxford science publications |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 226 S. graph. Darst. |
| ISBN: | 0198534671 |
Staff View
MARC
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| 100 | 1 | |a Baines, Michael J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Moving finite elements |c M. J. Baines |
| 264 | 1 | |a Oxford |b Clarendon |c 1994 | |
| 300 | |a XI, 226 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
I
1 The MFE Method of Miller 1
1.1 Introduction 1
1.2 The Fixed Finite Element Method 1
1.3 Time Dependent Nodes 5
1.4 Residual Minimization 7
1.5 Gradient Weighted MFE 9
1.6 Singularities and Penalty Functions 11
1.7 Boundary Conditions 13
1.8 Time Integration 13
1.9 Steady State 14
1.10 Examples 15
1.11 Systems of Equations 19
1.12 Summary and Notation 21
2 Transformations and Steep Fronts 23
2.1 Introduction 23
2.2 Grid Mappings and Equidistribution 23
2.3 The Time Derivative 25
2.4 Lagrangian Form 26
2.5 MFE Residual Minimization Revisited 28
2.6 The Legendre Transformation 30
2.7 Overturning Solutions and Sharp Fronts 34
2.8 The Nonlinear Heat Equation 39
3 Exact Semi Discrete MFE Solutions 41
3.1 Introduction 41
3.2 Discontinuous Linears in 1 D 41
3.3 Link with the Theory of PDEs 45
3.4 Legendre Fenchel Transformation 47
3.5 Overturning Solutions and Shocks 49
3.6 Examples 50
3.7 Semi discrete Solutions in the Dual Space 52
3.8 Exact Semi discrete Solutions in 2 D 54
3.9 Time Stepping 58
3.10 Higher Order Approximation 58
x CONTENTS
3.11 A Comment on Systems 59
3.12 Conclusion 60
4 MFE in 1 D: First order Equations 61
4.1 Introduction 61
4.2 Local Projection 61
4.3 Equivalence with Miller s Method 64
4.4 Decompositions of the MFE Mass Matrix 66
4.5 A Two stage Procedure 70
4.6 Equality Constraints 72
4.7 Linear Interpolant Projection 73
4.8 Approximate Shock Modelling 75
4.9 Examples 75
4.10 Element Motions in the Dual Space 78
5 MFE in 1 D: Second order Equations 80
5.1 Introduction 80
5.2 Nodal Speeds for the Linear Heat Equation 80
5.3 GWMFE Inner Products 86
5.4 The Nonlinear Heat Equation 87
5.5 Second Order Operators and Recovery 88
5.6 Time stepping 90
5.7 Steady State 91
5.8 Convection Diffusion by MFE 92
5.9 Moving Boundaries 94
6 MFE in Higher Dimensions 96
6.1 Introduction 96
6.2 Exact Semi discrete Solutions in 2 D 98
6.3 The Local Approach in 2 D 99
6.4 Decomposition of the MFE Mass Matrix in 2 D 102
6.5 Inversion of the Mass Matrix 107
6.6 Miller s Diagonal Norm 110
6.7 Projection into the Legendre Dual Space in 2 D 112
6.8 Second Order Operators in 2 D 114
6.9 Conclusion 116
7 Results from the MFE Method 117
7.1 Introduction 117
7.2 Results from Explicit MFE 118
7.3 MFE Results from the CWI Group 122
7.4 Miller and Carlson s GWMFE Results 127
7.5 GWMFE and Graph Massage 132
7.6 Remarks 136
CONTENTS xi
II
8 The Role of the MFE Method 139
8.1 Introduction 139
8.2 Objectives 139
8.3 Approximate Characteristic Motions 141
8.4 A Best Fit Carrying Property of MFE 144
8.5 A Steady State Best Fit Property of MFE 146
8.6 Equidistribution 147
8.7 Discussion 147
9 Best Pits with Adjustable Nodes 149
9.1 Introduction 149
9.2 Piecewise Linear Fits in 1 D 150
9.3 An Algorithm for Linear Fits in 1 D 153
9.4 Piecewise Constant Fits in 1 D 159
9.5 Simplified Algorithms in 1 D 163
9.6 Piecewise Linear Fits in 2 D 165
9.7 An Algorithm for Linear Fits on Triangles 168
9.8 Piecewise Constant Fits in 2 D 172
9.9 Simplified Algorithms in 2 D 176
9.10 Equidistribution Results in 1 D 183
10 MFE and Moving Best Fits 185
10.1 Introduction 185
10.2 Suppression of Characteristic Speeds 187
10.3 The SMFE method 188
10.4 The MBF Method for Piecewise Linears 191
10.5 The MBF Method for Piecewise Constants 194
10.6 MBF Methods in 2 D 197
10.7 The MBF Method and MFE 197
11 Discussion and Conclusion 201
11.1 Introduction 201
11.2 Approximate Legendre Transformations 202
11.3 Variational Principles 205
11.4 Intersection/Averaging for Linears in 2 D 207
11.5 Error Analysis for MFE 209
11.6 Final Remarks 210
|
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| dewey-search | 515/.353 |
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| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV010544414 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:54:47Z |
| institution | BVB |
| isbn | 0198534671 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007027706 |
| oclc_num | 30974516 |
| open_access_boolean | |
| owner | DE-384 DE-29T DE-91 DE-BY-TUM DE-703 DE-634 DE-83 |
| owner_facet | DE-384 DE-29T DE-91 DE-BY-TUM DE-703 DE-634 DE-83 |
| physical | XI, 226 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Clarendon |
| record_format | marc |
| series2 | Monographs on numerical analysis Oxford science publications |
| spelling | Baines, Michael J. Verfasser aut Moving finite elements M. J. Baines Oxford Clarendon 1994 XI, 226 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on numerical analysis Oxford science publications Eindige-elementenmethode gtt Partiële differentiaalvergelijkingen gtt element fini inriac frontiere libre inriac methode MFE inriac Éléments finis, Méthode des ram Differential equations, Partial Numerical solutions Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007027706&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baines, Michael J. Moving finite elements Eindige-elementenmethode gtt Partiële differentiaalvergelijkingen gtt element fini inriac frontiere libre inriac methode MFE inriac Éléments finis, Méthode des ram Differential equations, Partial Numerical solutions Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4017233-8 |
| title | Moving finite elements |
| title_auth | Moving finite elements |
| title_exact_search | Moving finite elements |
| title_full | Moving finite elements M. J. Baines |
| title_fullStr | Moving finite elements M. J. Baines |
| title_full_unstemmed | Moving finite elements M. J. Baines |
| title_short | Moving finite elements |
| title_sort | moving finite elements |
| topic | Eindige-elementenmethode gtt Partiële differentiaalvergelijkingen gtt element fini inriac frontiere libre inriac methode MFE inriac Éléments finis, Méthode des ram Differential equations, Partial Numerical solutions Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Eindige-elementenmethode Partiële differentiaalvergelijkingen element fini frontiere libre methode MFE Éléments finis, Méthode des Differential equations, Partial Numerical solutions Finite element method Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007027706&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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