A variational inequality approach to free boundary problems with applications in mould filling:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2002
|
| Schriftenreihe: | International series of numerical mathematics
136 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009638527&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 294 S. graph. Darst. |
| ISBN: | 376436582X |
Internformat
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| 245 | 1 | 0 | |a A variational inequality approach to free boundary problems with applications in mould filling |c Jörg Steinbach |
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Datensatz im Suchindex
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| adam_text | A VARIATIONAL INEQUALITY APPROACH TO FREE BOUNDARY PROBLEMS WITH
APPLICATIONS IN MOULD FILLING JORG STEINBACH BIRKHAUSER VERLAG BASEL *
BOSTON * BERLIN CONTENTS PREFACE IX 1 INTRODUCTION 2 EVOLUTIONARY
VARIATIONAL INEQUALITY APPROACH 2.1 THE DEGENERATE FREE BOUNDARY PROBLEM
8 2.2 SOME APPLICATION PROBLEMS 10 2.3 DIFFERENT FIXED DOMAIN
FORMULATIONS 18 2.3.1 FRONT TRACKING AND FIXING METHODS VERSUS FIXED
DOMAIN FORMULATIONS EXEMPLIFIED BY INJECTION AND COMPRESSION MOULDING 18
2.3.2 WEAK FORMULATION 19 2.3.3 THE EVOLUTIONARY VARIATIONAL INEQUALITY
APPROACH 23 3 PROPERTIES OF THE VARIATIONAL INEQUALITY SOLUTION 3.1
PROBLEM SETTING AND GENERAL NOTATIONS 32 3.2 EXISTENCE AND UNIQUENESS
RESULT 36 3.3 MONOTONICITY PROPERTIES AND REGULARITY WITH RESPECT TO
TIME ... 40 3.3.1 TIME-INDEPENDENT CONVEX SETS 40 3.3.2 TIME-DEPENDENT
CONVEX SETS .-**.-* 46 3.4 REGULARITY WITH RESPECT TO SPACE VARIABLES .
55 3.4.1 DIRICHLET BOUNDARY CONDITIONS 56 3.4.2 BOUNDARY CONDITIONS OF
NEUMANN/NEWTON TYPE 63 3.5 SOME REMARKS ON FURTHER REGULARITY RESULTS 69
4 FINITE VOLUME APPROXIMATIONS FOR ELLIPTIC INEQUALITIES 4.1 FINITE
ELEMENT AND VOLUME APPROXIMATIONS FOR THE OBSTACLE PROBLEM 74 4.1.1 THE
ELLIPTIC OBSTACLE PROBLEM 74 4.1.2 FINITE ELEMENT APPROXIMATIONS FOR THE
OBSTACLE PROBLEM 76 4.1.3 BASICS OF FINITE VOLUME APPROXIMATIONS 80
4.1.4 FINITE VOLUME APPROXIMATIONS FOR THE OBSTACLE PROBLEM 86 VI
CONTENTS 4.2 COMPARISON OF FINITE VOLUME AND FINITE ELEMENT
APPROXIMATIONS 93 4.3 ERROR ESTIMATES FOR THE FINITE VOLUME SOLUTION 103
4.4 PENALIZATION METHODS FOR THE FINITE VOLUME OBSTACLE PROBLEM ... 110
4.4.1 DISCRETE MAXIMUM PRINCIPLE 110 4.4.2 DISCUSSION OF PENALIZATION
TECHNIQUES ILL 4.4.3 ITERATIVE SOLUTION OF THE PENALIZATION PROBLEMS 122
4.5 THE SIGNORINI PROBLEM AS A BOUNDARY OBSTACLE PROBLEM 126 4.6 RESULTS
FROM NUMERICAL EXPERIMENTS FOR ELLIPTIC OBSTACLE PROBLEMS 131 4.6.1
EXAMPLES WITH KNOWN EXACT SOLUTION 132 4.6.2 NUMERICAL RESULTS FOR THE
ERROR BETWEEN THE FINITE ELEMENT AND THE FINITE VOLUME SOLUTION 135
4.6.3 ERROR BEHAVIOUR OF THE FINITE VOLUME AND THE PENALIZATION
SOLUTIONS 137 5 NUMERICAL ANALYSIS OF THE EVOLUTIONARY INEQUALITIES 5.1
FINITE ELEMENT AND VOLUME APPROXIMATIONS FOR THE EVOLUTIONARY PROBLEMS
144 5.1.1 FORMULATION OF THE FINITE ELEMENT AND FINITE VOLUME
APPROXIMATIONS 145 5.1.2 PROPERTIES OF THE DISCRETE INEQUALITY PROBLEMS
149 5.1.3 TIME EVOLUTION OF THE FINITE VOLUME SOLUTION 156 5.2 ERROR
ESTIMATES FOR THE FINITE ELEMENT AND FINITE VOLUME SOLUTIONS - 157
5.2.1 - COMPARISON OF THE FINITE ELEMENT AND FINITE VOLUME
APPROXIMATIONS 158 5.2.2 A PRIORI ESTIMATES FOR THE FINITE ELEMENT AND
FINITE VOLUME SOLUTIONS 162 5.2.3 CONVERGENCE RATE FOR THE FINITE
ELEMENT AND FINITE VOLUME SOLUTIONS 170 5.3 PENALIZATION METHODS FOR THE
EVOLUTIONARY FINITE VOLUME INEQUALITIES 179 5.3.1 DISCUSSION OF
PENALIZATION TECHNIQUES . 179 5.3.2 ITERATIVE SOLUTION OF THE
PENALIZATION PROBLEMS 187 5.4 NUMERICAL EXPERIMENTS FOR EVOLUTIONARY
VARIATIONAL INEQUALITIES 191 5.4.1 TWO EVOLUTIONARY VARIATIONAL
INEQUALITIES AND THE RELATED FREE BOUNDARY PROBLEMS 192 5.4.2 NUMERICAL
RESULTS FOR THE ERRORS BETWEEN EXACT, FINITE ELEMENT AND FINITE VOLUME
SOLUTION 194 5.4.3 ERROR BEHAVIOUR OF THE PENALIZATION SOLUTIONS 199
CONTENTS VII 6 INJECTION AND COMPRESSION MOULDING AS APPLICATION
PROBLEMS 6.1 CLASSICAL HELE-SHAW FLOWS AND RELATED MOVING BOUNDARY
PROBLEMS 204 6.2 MATHEMATICAL MODELLING OF INJECTION AND COMPRESSION
MOULDING 206 6.2.1 INJECTION AND COMPRESSION MOULDING - TECHNICAL
BACKGROUND AND REQUIREMENTS ON SIMULATION 207 6.2.1.1 TECHNICAL
BACKGROUND 207 6.2.1.2 SHORT COMPARISON OF INJECTION/COMPRESSION
MOULDING AND METAL CASTING 209 6.2.1.3 SOME AIMS OF THE NUMERICAL
SIMULATION 210 6.2.2 BALANCE AND STATE EQUATIONS 212 6.2.3 RHEOLOGICAL
BEHAVIOUR OF POLYMER MELTS 213 6.2.4 TEMPERATURE-DEPENDENT HELE-SHAW
FLOW IN THE INJECTION AND COMPRESSION MOULDING PROCESS 217 6.2.4.1 THE
GENERALIZED HELE-SHAW FLOW 217 6.2.4.2 VISCOSITY MODELS AND
NON-ISOTHERMAL EFFECTS . . . 221 6.2.4.3 THE NUMERICAL CORE PROBLEMS 224
6.2.5 THE DISTANCE CONCEPT - A GEOMETRICAL APPROACH FOR INJECTION
MOULDING 225 6.2.6 RECENT THREE-DIMENSIONAL SIMULATION DEVELOPMENTS . .
. . 231 6.3 SIMULATION RESULTS 238 6.3.1 VARIATION OF GATE LOCATION AND
THICKNESS, NON-ISOTHERMAL EFFECTS, NARROW FLOW REGION 238 6.3.2
COMPARISON WITH THE DISTANCE MODEL 246 6.3.3 COMPARISON WITH
THREE-DIMENSIONAL SIMULATIONS 252 7 CONCLUDING-REMARKS BIBLIOGRAPHY * *
* 263 LIST OF FIGURES 277 LIST OF TABLES 279 LIST OF SYMBOLS 281 INDEX
289
|
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| indexdate | 2024-12-20T10:58:39Z |
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| isbn | 376436582X |
| language | English |
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| publisher | Birkhäuser |
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| series | International series of numerical mathematics |
| series2 | International series of numerical mathematics |
| spellingShingle | Steinbach, Jörg A variational inequality approach to free boundary problems with applications in mould filling International series of numerical mathematics Mathematisches Modell Boundary value problems Numerical solutions Differential equations, Nonlinear Numerical solutions Elliptic operators Plastics Molding Mathematical models Variational inequalities (Mathematics) Variationsungleichung (DE-588)4187420-1 gnd Spritzgießen (DE-588)4056561-0 gnd Freies Randwertproblem (DE-588)4155303-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4187420-1 (DE-588)4056561-0 (DE-588)4155303-2 (DE-588)4114528-8 (DE-588)4044779-0 |
| title | A variational inequality approach to free boundary problems with applications in mould filling |
| title_auth | A variational inequality approach to free boundary problems with applications in mould filling |
| title_exact_search | A variational inequality approach to free boundary problems with applications in mould filling |
| title_full | A variational inequality approach to free boundary problems with applications in mould filling Jörg Steinbach |
| title_fullStr | A variational inequality approach to free boundary problems with applications in mould filling Jörg Steinbach |
| title_full_unstemmed | A variational inequality approach to free boundary problems with applications in mould filling Jörg Steinbach |
| title_short | A variational inequality approach to free boundary problems with applications in mould filling |
| title_sort | a variational inequality approach to free boundary problems with applications in mould filling |
| topic | Mathematisches Modell Boundary value problems Numerical solutions Differential equations, Nonlinear Numerical solutions Elliptic operators Plastics Molding Mathematical models Variational inequalities (Mathematics) Variationsungleichung (DE-588)4187420-1 gnd Spritzgießen (DE-588)4056561-0 gnd Freies Randwertproblem (DE-588)4155303-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Mathematisches Modell Boundary value problems Numerical solutions Differential equations, Nonlinear Numerical solutions Elliptic operators Plastics Molding Mathematical models Variational inequalities (Mathematics) Variationsungleichung Spritzgießen Freies Randwertproblem Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009638527&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035415862 |
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