Multiscale and adaptivity: modeling, numerics and applications: C.I.M.E. summer school, Cetraro, Italy 2009
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| Other Authors: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2012
|
| Series: | Lecture notes in mathematics
2040 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XII, 314 S. teilw farb. graph. Darst. 24 cm |
| ISBN: | 9783642240782 364224078X 9783642240799 |
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MARC
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Record in the Search Index
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IMAGE 1
CONTENTS
ADAPTIVE WAVELET METHODS 1
SILVIA BERTOLUZZA 1 INTRODUCTION 1
2 MULTIRESOLUTION APPROXIMATION AND WAVELETS 2
2.1 RIESZ BASES 2
2.2 MULTIRESOLUTION ANALYSIS 3
2.3 EXAMPLES 9
2.4 BEYOND L 2 (R) 17
3 THE FUNDAMENTAL PROPERTY OF WAVELETS 21
3.1 THE CASE Q = R: THE FREQUENCY DOMAIN POINT OF VIEW VS. THE SPACE
DOMAIN POINT OF VIEW 22
4 ADAPTIVE WAVELET METHODS FOR PDE'S: THE FIRST GENERATION 34 4.1 THE
ADAPTIVE WAVELET COLLOCATION METHOD 37
5 THE NEW GENERATION OF ADAPTIVE WAVELET METHODS 40
5.1 A POSTERIORI ERROR ESTIMATES 41
5.2 NONLINEAR WAVELET METHODS FOR THE SOLUTION OF PDE'S 46 5.3 THE CDD2
ALGORITHM 48
5.4 OPERATIONS ON INFINITE MATRICES AND VECTORS 51
REFERENCES 54
HETEROGENEOUS MATHEMATICAL MODELS IN FLUID DYNAMICS AND ASSOCIATED
SOLUTION ALGORITHMS 57
MARCO DISCACCIATI, PAOLA GERVASIO, AND ALFIO QUARTERONI 1 INTRODUCTION
AND MOTIVATION 57
2 VARIATIONAL FORMULATION APPROACH 67
2.1 THE ADVECTION-DIFFUSION PROBLEM 67
2.2 VARIATIONAL ANALYSIS FOR THE ADVECTION-DIFFUSION EQUATION 68 2.3
DOMAIN DECOMPOSITION ALGORITHMS FOR THE SOLUTION OF THE REDUCED
ADVECTION-DIFFUSION PROBLEM 72
2.4 NUMERICAL RESULTS FOR THE ADVECTION-DIFFUSION PROBLEM 77 2.5
NAVIER-STOKES/POTENTIAL COUPLED PROBLEM 80
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1014483867
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
2.6 ASYMPTOTIC ANALYSIS OF THE COUPLED NAVIER-STOKES/ DARCY PROBLEM 82
2.7 SOLUTION TECHNIQUES FOR THE NAVIER-STOKES/DARCY COUPLING 85 2.8
NUMERICAL RESULTS FOR THE NAVIER-STOKES/DARCY PROBLEM 90 3 VIRTUAL
CONTROL APPROACH 94
3.1 VIRTUAL CONTROL APPROACH WITHOUT OVERLAP FOR AD PROBLEMS 95 3.2
DOMAIN DECOMPOSITION WITH OVERLAP 105
3.3 VIRTUAL CONTROL APPROACH WITH OVERLAP FOR THE ADVECTION-DIFFUSION
EQUATION 108
3.4 VIRTUAL CONTROL WITH OVERLAP FOR THE STOKES-DARCY COUPLING 114
3.5 COUPLING FOR INCOMPRESSIBLE FLOWS 119
REFERENCES 120
PRIMER OF ADAPTIVE FINITE ELEMENT METHODS 125
RICARDO H. NOCHETTO AND ANDREAS VEESER 1 PIECEWISE POLYNOMIAL
APPROXIMATION 125
1.1 CLASSICAL VS ADAPTIVE POINTWISE APPROXIMATION 126
1.2 THE SOBOLEV NUMBER: SCALING AND EMBEDDING 127
1.3 CONFORMING MESHES: THE BISECTION METHOD 129
1.4 FINITE ELEMENT SPACES 133
1.5 POLYNOMIAL INTERPOLATION IN SOBOLEV SPACES 134
1.6 ADAPTIVE APPROXIMATION 139
1.7 NONCONFORMING MESHES 143
1.8 NOTES 145
1.9 PROBLEMS 146
2 ERROR BOUNDS FOR FINITE ELEMENT SOLUTIONS 148
2.1 MODEL BOUNDARY VALUE PROBLEM 148
2.2 GALERKIN SOLUTIONS 149
2.3 FINITE ELEMENT SOLUTIONS AND A PRIORI BOUND 150
2.4 A POSTERIORI UPPER BOUND 151
2.5 NOTES 157
2.6 PROBLEMS 158
3 LOWER A POSTERIORI BOUNDS 159
3.1 LOCAL LOWER BOUNDS 160
3.2 GLOBAL LOWER BOUND 166
3.3 NOTES 167
3.4 PROBLEMS 168
4 CONVERGENCE OF AFEM 170
4.1 A MODEL ADAPTIVE ALGORITHM 171
4.2 CONVERGENCE 172
4.3 NOTES 178
4.4 PROBLEMS 179
5 CONTRACTION PROPERTY OF AFEM 180
5.1 MODULES OF AFEM FOR THE MODEL PROBLEM 180
5.2 BASIC PROPERTIES OF AFEM 182
IMAGE 3
CONTENTS XI
5.3 CONTRACTION PROPERTY OF AFEM 185
5.4 EXAMPLE: DISCONTINUOUS COEFFICIENTS 189
5.5 EXTENSIONS AND RESTRICTIONS 191
5.6 NOTES 193
5.7 PROBLEMS 193
6 COMPLEXITY OF REFINEMENT 194
6.1 CHAINS AND LABELING FOR D = 2 195
6.2 RECURSIVE BISECTION 197
6.3 CONFORMING MESHES: PROOF OF THEOREM 1 199
6.4 NONCONFORMING MESHES: PROOF OF LEMMA 3 204
6.5 NOTES 205
6.6 PROBLEMS 206
7 CONVERGENCE RATES 206
7.1 THE TOTAL ERROR 207
7.2 APPROXIMATION CLASSES 208
7.3 QUASI-OPTIMAL CARDINALITY: VANISHING OSCILLATION 212 7.4
QUASI-OPTIMAL CARDINALITY: GENERAL DATA 215
7.5 EXTENSIONS AND RESTRICTIONS 218
7.6 NOTES 221
7.7 PROBLEMS 221
REFERENCES 223
MATHEMATICALLY FOUNDED DESIGN OF ADAPTIVE FINITE ELEMENT SOFTWARE 227
KUNIBERT G. SIEBERT 1 INTRODUCTION 227
1.1 THE VARIATIONAL PROBLEM 229
1.2 THE BASIC ADAPTIVE ALGORITHM 230
2 TRIANGULATIONS AND FINITE ELEMENT SPACES 232
2.1 TRIANGULATIONS 232
2.2 FINITE ELEMENT SPACES 234
2.3 BASIS FUNCTIONS AND EVALUATION OF FINITE ELEMENT FUNCTIONS 240
2.4 ALBERTA REALIZATION OF FINITE ELEMENT SPACES 244
3 REFINEMENT BY BISECTION 246
3.1 BASIC THOUGHTS ABOUT LOCAL REFINEMENT 246
3.2 BISECTION RULE: BISECTION OF ONE SINGLE SIMPLEX 248
3.3 TRIANGULATIONS AND REFINEMENTS 252
3.4 REFINEMENT ALGORITHMS 255
3.5 COMPLEXITY OF REFINEMENT BY BISECTION 260
3.6 ALBERTA REFINEMENT 262
3.7 MESH TRAVERSAL ROUTINES 263
4 ASSEMBLAGE OF THE LINEAR SYSTEM 268
4.1 THE VARIATIONAL PROBLEM AND THE LINEAR SYSTEM 269
4.2 ASSEMBLAGE: THE OUTER LOOP 272
IMAGE 4
XII CONTENTS
4.3 ASSEMBLAGE: ELEMENT INTEGRALS 276
4.4 REMARKS ON ITERATIVE SOLVERS 283
5 THE ADAPTIVE ALGORITHM AND CONCLUDING REMARKS 285
5.1 THE ADAPTIVE ALGORITHM 286
5.2 CONCLUDING REMARKS 294
6 SUPPLEMENT: A NONLINEAR AND A SADDLEPOINT PROBLEM 297
6.1 THE PRESCRIBED MEAN CURVATURE PROBLEM IN GRAPH FORMULATION 297 6.2
THE GENERALIZED STOKES PROBLEM 301
REFERENCES 308
LIST OF PARTICIPANTS 311 |
| any_adam_object | 1 |
| author2 | Naldi, Giovanni |
| author2_role | edt |
| author2_variant | g n gn |
| author_GND | (DE-588)1020162023 (DE-588)1020162678 |
| author_facet | Naldi, Giovanni |
| building | Verbundindex |
| bvnumber | BV039857554 |
| classification_rvk | SI 850 |
| classification_tum | PHY 220f MAT 428f MAT 671f |
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| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| genre_facet | Konferenzschrift 2009 Cetraro |
| id | DE-604.BV039857554 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:22:53Z |
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| isbn | 9783642240782 364224078X 9783642240799 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Multiscale and adaptivity: modeling, numerics and applications C.I.M.E. summer school, Cetraro, Italy 2009 Silvia Bertoluzza ... Ed.: Giovanni Naldi ... Berlin [u.a.] Springer 2012 XII, 314 S. teilw farb. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2040 : CIME Foundation subseries Literaturangaben Mehrskalenmodell (DE-588)7600619-0 gnd rswk-swf Adaptives Verfahren (DE-588)4310560-9 gnd rswk-swf Mehrskalenanalyse (DE-588)4416235-2 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2009 Cetraro gnd-content Mehrskalenanalyse (DE-588)4416235-2 s Mehrskalenmodell (DE-588)7600619-0 s Numerisches Verfahren (DE-588)4128130-5 s Adaptives Verfahren (DE-588)4310560-9 s DE-604 Bertoluzza, Silvia Sonstige (DE-588)1020162023 oth Naldi, Giovanni (DE-588)1020162678 edt Centro Internazionale Matematico Estivo Sonstige (DE-588)1025933-8 oth Erscheint auch als Online-Ausgabe Multiscale and Adaptivity: Modeling, Numerics and Applications Lecture notes in mathematics 2040 (DE-604)BV000676446 2040 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3869555&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=024717177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Multiscale and adaptivity: modeling, numerics and applications C.I.M.E. summer school, Cetraro, Italy 2009 Lecture notes in mathematics Mehrskalenmodell (DE-588)7600619-0 gnd Adaptives Verfahren (DE-588)4310560-9 gnd Mehrskalenanalyse (DE-588)4416235-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)7600619-0 (DE-588)4310560-9 (DE-588)4416235-2 (DE-588)4128130-5 (DE-588)1071861417 |
| title | Multiscale and adaptivity: modeling, numerics and applications C.I.M.E. summer school, Cetraro, Italy 2009 |
| title_auth | Multiscale and adaptivity: modeling, numerics and applications C.I.M.E. summer school, Cetraro, Italy 2009 |
| title_exact_search | Multiscale and adaptivity: modeling, numerics and applications C.I.M.E. summer school, Cetraro, Italy 2009 |
| title_full | Multiscale and adaptivity: modeling, numerics and applications C.I.M.E. summer school, Cetraro, Italy 2009 Silvia Bertoluzza ... Ed.: Giovanni Naldi ... |
| title_fullStr | Multiscale and adaptivity: modeling, numerics and applications C.I.M.E. summer school, Cetraro, Italy 2009 Silvia Bertoluzza ... Ed.: Giovanni Naldi ... |
| title_full_unstemmed | Multiscale and adaptivity: modeling, numerics and applications C.I.M.E. summer school, Cetraro, Italy 2009 Silvia Bertoluzza ... Ed.: Giovanni Naldi ... |
| title_short | Multiscale and adaptivity: modeling, numerics and applications |
| title_sort | multiscale and adaptivity modeling numerics and applications c i m e summer school cetraro italy 2009 |
| title_sub | C.I.M.E. summer school, Cetraro, Italy 2009 |
| topic | Mehrskalenmodell (DE-588)7600619-0 gnd Adaptives Verfahren (DE-588)4310560-9 gnd Mehrskalenanalyse (DE-588)4416235-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Mehrskalenmodell Adaptives Verfahren Mehrskalenanalyse Numerisches Verfahren Konferenzschrift 2009 Cetraro |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3869555&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=024717177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT bertoluzzasilvia multiscaleandadaptivitymodelingnumericsandapplicationscimesummerschoolcetraroitaly2009 AT naldigiovanni multiscaleandadaptivitymodelingnumericsandapplicationscimesummerschoolcetraroitaly2009 AT centrointernazionalematematicoestivo multiscaleandadaptivitymodelingnumericsandapplicationscimesummerschoolcetraroitaly2009 |