Finite element methods for integrodifferential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1998
|
| Series: | Series on applied mathematics
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 272 S. |
| ISBN: | 9810232632 |
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MARC
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| 245 | 1 | 0 | |a Finite element methods for integrodifferential equations |c Chen Chuanmiao ; Shih Tsimin |
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Record in the Search Index
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| adam_text | Contents
Preface v
Notations xi
1. Some Practical Problems and Their Properties 1
1.1. Heat Conduction in Materials with Memory 2
1.2. Viscoelasticity 6
1.3. Reactor Dynamics 11
1.4. Reduction of a Coupled System 14
2. Parabolic Integrodifferential Equations 17
2.1. Solvability in Spaces L2, V and Cn 17
2.2. Semigroup Method 25
3. A Survey on Elliptic Finite Elements 35
3.1. Elliptic Projection i?/,w 35
3.2. Domains with Curvilinear Boundaries 41
3.3. Ritz Volterra Projection VhU 4G
4. Semidiscrete and Fully Discrete Schemes 53
4.1. Semidiscretization 53
4.2. Full Discretization 59
4.3. The Lumped Mass Method 67
xv
xvi Contents
5. Saving of Storage 71
5.1. Economic Backward Euler Scheme (EBES) 71
5.2. Economic Crank Nicolson Scheme (ECNS) 75
5.3. Additive Schemes 80
6. Cases with Nonsmooth Initial Values 85
6.1. Regularities of the Solution 85
6.2. Error Estimates for Semidiscretization 94
6.3. Backward Euler Scheme 106
7. Cases with Weakly Singular Kernels 117
7.1. Continuous Problems 117
7.2. Discretization in Space 122
7.3. The Completely Discrete Scheme 127
7.4. Cases with Nonsmooth Data 131
8. Long time Estimates 139
8.1. Continuous Problems 140
8.2. Backward Euler Scheme for B = A 142
8.3. Second Order Backward Difference Method for B = A 147
8.4. The General Case for B 150
8.5. Application to Finite Element Discretization in Space 154 ,
9. Maximum Norm Estimates 157
9.1. L°° Estimates of Ritz Volterra Projection 157
9.2. Estimates for Semidiscretization 166
9.3. Complete Discretization 170
10. Superconvergence 173
10.1. The Energy Method 173
10.2. Gradient Type Green Function 180
10.3. Applications of Superconvergence and Extrapolation 186
Contents xvii
11. Nonlinear Problems 193
11.1. Strongly Nonlinear Cases and the Green Function Method .... 197
11.2. Weakly Nonlinear Cases and the Energy Method 200
11.3. Solution to System of Nonlinear Equations 204
12. Hyperbolic Problems 209
12.1. Solvability of Linear Problems 209
12.2. Discretization for Linear Problem 215
12.3. Nonlinear Cases 222
13. Problems with Positive Memory 227
13.1. Regularity of the Solution 228
13.2. Semidiscretization in Space 234
13.3. Positive Definite Quadrature Rules 236
13.4. Full Discretization 242
References 255
Index 271
|
| any_adam_object | 1 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:23:19Z |
| institution | BVB |
| isbn | 9810232632 |
| language | English |
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| owner_facet | DE-703 DE-83 |
| physical | XVII, 272 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on applied mathematics |
| series2 | Series on applied mathematics |
| spelling | Chen, Chuanmiao Verfasser aut Finite element methods for integrodifferential equations Chen Chuanmiao ; Shih Tsimin Singapore [u.a.] World Scientific 1998 XVII, 272 S. txt rdacontent n rdamedia nc rdacarrier Series on applied mathematics 9 Finite element method Integro-differential equations Numerical solutions Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Integrodifferentialgleichung (DE-588)4161939-0 gnd rswk-swf Integrodifferentialgleichung (DE-588)4161939-0 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Shih, Tsimin Verfasser aut Series on applied mathematics 9 (DE-604)BV007228284 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008260540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Chuanmiao Shih, Tsimin Finite element methods for integrodifferential equations Series on applied mathematics Finite element method Integro-differential equations Numerical solutions Finite-Elemente-Methode (DE-588)4017233-8 gnd Integrodifferentialgleichung (DE-588)4161939-0 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4161939-0 |
| title | Finite element methods for integrodifferential equations |
| title_auth | Finite element methods for integrodifferential equations |
| title_exact_search | Finite element methods for integrodifferential equations |
| title_full | Finite element methods for integrodifferential equations Chen Chuanmiao ; Shih Tsimin |
| title_fullStr | Finite element methods for integrodifferential equations Chen Chuanmiao ; Shih Tsimin |
| title_full_unstemmed | Finite element methods for integrodifferential equations Chen Chuanmiao ; Shih Tsimin |
| title_short | Finite element methods for integrodifferential equations |
| title_sort | finite element methods for integrodifferential equations |
| topic | Finite element method Integro-differential equations Numerical solutions Finite-Elemente-Methode (DE-588)4017233-8 gnd Integrodifferentialgleichung (DE-588)4161939-0 gnd |
| topic_facet | Finite element method Integro-differential equations Numerical solutions Finite-Elemente-Methode Integrodifferentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008260540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007228284 |
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