Adaptive finite elements in the discretization of parabolic problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Logos
2011
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| Schriftenreihe: | Augsburger Schriften zur Mathematik, Physik und Informatik
15 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | VIII, 248 S. Ill., graph. Darst. |
| ISBN: | 9783832528157 |
Internformat
MARC
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| 245 | 1 | 0 | |a Adaptive finite elements in the discretization of parabolic problems |c vorgelegt von Christian A. Möller |
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| 300 | |a VIII, 248 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a Augsburger Schriften zur Mathematik, Physik und Informatik |v 15 | |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
INTRODUCTION 1 1.1 OUTLINE OF THE THESIS 41.2 NOTATION AND FUNCTION
SPACES 51.2.1 SPACES ON BOUNDED DOMAINS 51.2.2 SPACES INVOLVING TIME
9ANALYSIS OF PARABOLIC PDES 132.1 WEAK FORMULATION 152.2 EXISTENCE AND
UNIQUENESS OF A SOLUTION 24 2.3 STABILITY ESTIMATE . 36 DISCRETIZATION
OF PARABOLIC PDES 43 3.1 TRIANGULATIONS AND FINITE ELEMENT SPACES 43
3.1.1 REFINEMENT AND COARSENING 473.1.2 FINITE ELEMENT SPACES 543.2
SPACE TIME DISCRETIZATION 593.2.1 SPATIAL DISCRETIZATION 603.2.2 FULL
SPACE TIME DISCRETIZATION 61 3.3 ADAPTIVE METHODS FOR ELLIPTIC PROBLEMS
64 3.3.1 EXISTENCE AND UNIQUENESS 653.3.2 GALERKIN DISCRETIZATION
673.3.3 A PRIORI ERROR ANALYSIS 683.3.4 A POSTERIORI ERROR ANALYSIS
693.3.5 ADAPTIVITY FOR STATIONARY PROBLEMS 76 3.4 A POSTERIORI ANALYSIS
81 3.4.1 UPPER BOUND 853.4.2 LOWER BOUND 91 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/1010994786 DIGITALISIERT DURCH
IMAGE 2
VI CONTENTS
4 THE ADAPTIVE ALGORITHM ASTFEM 105
4.1 PRINCIPLES OF ERROR CONTROL 108
4.1.1 RE-DEFINITION OF ERROR INDICATORS 108
4.1.2 UNIFORM BOUND ON INDICATORS 110
4.1.3 ERROR CONTROL VIA ENERGY ESTIMATE 113
4.2 ESTABLISHING ERROR CONTROL 123
4.2.1 ENERGY GAIN 124
4.2.2 INITIAL ERROR INDICATOR 125
4.2.3 CONSISTENCY ERROR INDICATOR 126
4.2.4 SPACE ERROR INDICATOR 128
4.2.5 COARSEN-TIME ERROR INDICATOR 128
4.2.6 COUPLING EFFECTS 133
4.2.7 ESTABLISHING ERROR CONTROL FOR COUPLED INDICA- TORS 136
4.3 ERROR CONTROL IN ASTFEM 139
4.3.1 COMPARISON OF ERROR CONTROL STRATEGIES . . . 139 4.3.2 JOINT
ERROR CONTROL 141
4.4 STRUCTURE OF ASTFEM 145
4.4.1 PRELIMINARIES 146
4.4.2 A SINGLE TIME STEP 147
4.5 TERMINATION AND CONVERGENCE INTO TOLERANCE 156 4.6 REALIZATION OF
THE ABSTRACT MODULES 160
4.6.1 THE MODULE CONSISTENCY 160
4.6.2 THE MODULE ST_ADAPTATI0N 162
5 NUMERICAL ASPECTS OF ASTFEM 169
5.1 COARSENING IN ASTFEM 169
5.1.1 UNIFORM COARSENING 171
5.1.2 ADAPTIVE COARSENING 171
5.2 COMPARISON WITH CLASSICAL ALGORITHM 183
5.3 NUMERICAL RESULTS 188
6 APPLICATION TO CARBONATION PROBLEM 199
6.1 OVERVIEW OF CONCRETE CARBONATION 199
6.2 DERIVATION OF THE MACROSCOPIC MODEL 201
6.2.1 THE PORE-SCALE CARBONATION MODEL 202
6.2.2 NON-DIMENSIONALIZATION 203
6.2.3 TRANSFORMATION TO AN E-PERIODIC REFERENCE CON- FIGURATION 205
IMAGE 3
CONTENTS
6.2.4 COUPLING THE REACTION-DIFFUSION SYSTEM AND THE EVOLUTION OF THE
MICROSTRUCTURE 209 6.3 DISCRETIZATION 210
6.3.1 WEAK FORMULATION OF THE PDE 211
6.3.2 OBJECTIVE OF THE DISCRETIZATION 213
6.3.3 COUPLED DISCRETIZATION 214
6.3.4 DECOUPLED DISCRETIZATION 217
6.4 IMPLEMENTATION 219
6.5 NUMERICAL RESULTS 225
6.5.1 PARAMETER VALUES 226
6.5.2 INTERPRETATION OF THE RESULTS 227
6.5.3 COMPARISON OF THE DIFFERENT DISCRETIZATIONS . . 231 6.6
CONCLUSIONS AND OUTLOOK 238 |
| any_adam_object | 1 |
| author | Möller, Christian A. 1983- |
| author_GND | (DE-588)14404790X |
| author_facet | Möller, Christian A. 1983- |
| author_role | aut |
| author_sort | Möller, Christian A. 1983- |
| author_variant | c a m ca cam |
| building | Verbundindex |
| bvnumber | BV037431976 |
| classification_rvk | SK 920 |
| ctrlnum | (OCoLC)725219979 (DE-599)DNB1010994786 |
| dewey-full | 518.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.64 |
| dewey-search | 518.64 |
| dewey-sort | 3518.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV037431976 |
| illustrated | Illustrated |
| indexdate | 2024-09-06T00:18:51Z |
| institution | BVB |
| isbn | 9783832528157 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022584040 |
| oclc_num | 725219979 |
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| owner_facet | DE-634 DE-384 DE-188 |
| physical | VIII, 248 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Logos |
| record_format | marc |
| series | Augsburger Schriften zur Mathematik, Physik und Informatik |
| series2 | Augsburger Schriften zur Mathematik, Physik und Informatik |
| spelling | Möller, Christian A. 1983- Verfasser (DE-588)14404790X aut Adaptive finite elements in the discretization of parabolic problems vorgelegt von Christian A. Möller Berlin Logos 2011 VIII, 248 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Augsburger Schriften zur Mathematik, Physik und Informatik 15 Zugl.: Augsburg, Univ., Diss., 2010 Adaptives Verfahren (DE-588)4310560-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Parabolische Differentialgleichung (DE-588)4173245-5 s Finite-Elemente-Methode (DE-588)4017233-8 s Adaptives Verfahren (DE-588)4310560-9 s DE-604 Augsburger Schriften zur Mathematik, Physik und Informatik 15 (DE-604)BV017601953 15 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3711632&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022584040&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Möller, Christian A. 1983- Adaptive finite elements in the discretization of parabolic problems Augsburger Schriften zur Mathematik, Physik und Informatik Adaptives Verfahren (DE-588)4310560-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4310560-9 (DE-588)4017233-8 (DE-588)4173245-5 (DE-588)4113937-9 |
| title | Adaptive finite elements in the discretization of parabolic problems |
| title_auth | Adaptive finite elements in the discretization of parabolic problems |
| title_exact_search | Adaptive finite elements in the discretization of parabolic problems |
| title_full | Adaptive finite elements in the discretization of parabolic problems vorgelegt von Christian A. Möller |
| title_fullStr | Adaptive finite elements in the discretization of parabolic problems vorgelegt von Christian A. Möller |
| title_full_unstemmed | Adaptive finite elements in the discretization of parabolic problems vorgelegt von Christian A. Möller |
| title_short | Adaptive finite elements in the discretization of parabolic problems |
| title_sort | adaptive finite elements in the discretization of parabolic problems |
| topic | Adaptives Verfahren (DE-588)4310560-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Adaptives Verfahren Finite-Elemente-Methode Parabolische Differentialgleichung Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3711632&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022584040&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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