Superconvergence in Galerkin finite element methods:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1995
|
| Schriftenreihe: | Lecture notes in mathematics
1605 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006774512&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 166 S. graph. Darst. |
| ISBN: | 3540600116 0387600116 |
Internformat
MARC
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| 100 | 1 | |a Wahlbin, Lars B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Superconvergence in Galerkin finite element methods |c Lars B. Wahlbin |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1995 | |
| 300 | |a XI, 166 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1605 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006774512 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 999-1605 |
|---|---|
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| DE-BY-TUM_location | 01 |
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| _version_ | 1821938523243020288 |
| adam_text | Table of Contents.
Chapter 1. Some one dimensional superconvergence results. 1
1.1. Introduction 1
1.2. Nodal superconvergence for function values in continuous
elements (fj, = 0). 3
1.3. Reduction to a model problem. 4
1.4. Existence of superconvergence points in general. 8
1.5. Superconvergence for interior points of mesh intervals for
continuous elements (fi = 0). 8
1.6. Superconvergence in derivatives at points about which the
meshs are locally symmetric (r even). 10
1.7. Necessity of staying Cihlnl/h away from the boundary for
superconvergence in the uniform mesh case (fj, = 1). 13
1.8. Finding all superconvergent points for function values and
derivatives in the case of a locally uniform mesh for /j, = 1
and r even (with a remark about smoothest cubics). 14
1.9. Superconvergence in function values at points about which
the meshes are locally symmetric (r odd). 16
1.10. Finding all superconvergent points for function values and
derivatives in the case of a locally uniform mesh for fi = 1 and
r odd. 19
1.11. First order difference quotients of «/, as superconvergent
approximations to v! on locally uniform meshes. 22
1.12. Two examples of superconvergence by iteration . 25
1.13. A graphical illustration of superconvergence. 26
Chapter 2. Remarks about some of the tools used in Chapter 1. 28
2.1. Inverse estimates. 28
2.2. On approximation theory, and duality. 30
2.3. Superapproximation. 32
2.4. A typical combination of inverse estimates and
approximation theory used in Chapter 1. 35
Chapter 3. Local and global properties of L2 projections. 36
3.1. Assumptions. 36
3.2. Estimates for L2 projections. 38
Chapter 4. Introduction to several space dimensions: some results
about superconvergence in 1,2 projections. 42
4.1. Negative norm estimates and existence of general
superconvergence points for function values. 42
4.2. Superconvergence in .Z^ projections on n dimensional
tensor product spaces. 43
4.3. Superconvergence by symmetry in £2 projections. 44
X
Chapter 5. Second order elliptic boundary value problems in any
number of space dimensions: preliminary considerations on local
and global estimates and presentation of the main technical tools
for showing superconvergence. 48
5.1. Introduction. 48
5.2. Existence of superconvergence points in general: an example
(also an example of a multi dimensional duality argument). 49
5.3. General comments on local a priori error estimates. 52
5.4. General comments on L^ estimates. 58
5.5. The main technical tools for proving superconvergence in
second order elliptic problems in several space dimensions. 62
Chapter 6. Superconvergence in tensor product elements. 65
6.1. Introduction. 65
6.2. Superconvergence in derivatives for the case of the Laplacian. 65
6.3. Negative norm estimates for u — u^: Examples. 69
6.4. Superconvergence in derivatives for the case of (6.1.1.). 70
6.5. Superconvergence in function values for the Laplacian and r 3. 72
Chapter 7. Superconvergence by local symmetry. 74
7.1. Introduction. 74
7.2. The case of a symmetric form with constant coefficients. 74
7.3. The general case of (5.1.3) with variable smooth coefficients. 78
7.4. Historical remarks. 79
Chapter 8. Superconvergence for difference quotients on translation
invariant meshes. 84
8.1. Introduction. 84
8.2. Constant coefficient operators and unit separation, d ~ 1. 86
8.3. Constant coefficient operators and general separation d. 89
8.4. Variable coefficients. 89
Chapter 9. On superconvergence in nonlinear problems. 93
Chapter 10. Superconvergence in isoparametric mappings of
translation invariant meshes: an example. 98
10.1. Introduction. 98
10.2. Superconvergence in difference quotients for first derivatives. 101
Chapter 11. Superconvergence by averaging: mainly, the .fif operator. 107
11.1. Introduction 107
11.2. Preliminaries on Fourier transforms and multipliers. 107
11.3. The /f operator in general. Ill
11.4. The .ftT operator applied to finite element approximations in
second order elliptic problems. 115
11.5. Boundary integral equations and the if operator: an example. 116
11.6. Remarks, including some other averaging methods. 121
11.7. A superconvergent global averaging technique for
function values. 123
xi
Chapter 12. A computational investigation of superconvergence
for first derivatives in the plane. 125
12.1. Introduction. 125
12.2. Proof of (12.1.5), (12.1.6) and precise definition of the principal
error term ip. 128
12.3. Results of computational studies, with comments. 132
References. 136
Subject index. 165
|
| any_adam_object | 1 |
| author | Wahlbin, Lars B. |
| author_facet | Wahlbin, Lars B. |
| author_role | aut |
| author_sort | Wahlbin, Lars B. |
| author_variant | l b w lb lbw |
| building | Verbundindex |
| bvnumber | BV010194802 |
| classification_rvk | SI 850 SK 920 |
| classification_tum | MAT 674f |
| ctrlnum | (OCoLC)231642714 (DE-599)BVBBV010194802 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010194802 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:49:44Z |
| institution | BVB |
| isbn | 3540600116 0387600116 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006774512 |
| oclc_num | 231642714 |
| open_access_boolean | |
| owner | DE-20 DE-824 DE-91G DE-BY-TUM DE-384 DE-12 DE-29T DE-355 DE-BY-UBR DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-20 DE-824 DE-91G DE-BY-TUM DE-384 DE-12 DE-29T DE-355 DE-BY-UBR DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XI, 166 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Wahlbin, Lars B. Superconvergence in Galerkin finite element methods Lecture notes in mathematics Elliptisches Randwertproblem (DE-588)4193399-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Galerkin-Methode (DE-588)4155831-5 gnd Konvergenz (DE-588)4032326-2 gnd |
| subject_GND | (DE-588)4193399-0 (DE-588)4017233-8 (DE-588)4155831-5 (DE-588)4032326-2 |
| title | Superconvergence in Galerkin finite element methods |
| title_auth | Superconvergence in Galerkin finite element methods |
| title_exact_search | Superconvergence in Galerkin finite element methods |
| title_full | Superconvergence in Galerkin finite element methods Lars B. Wahlbin |
| title_fullStr | Superconvergence in Galerkin finite element methods Lars B. Wahlbin |
| title_full_unstemmed | Superconvergence in Galerkin finite element methods Lars B. Wahlbin |
| title_short | Superconvergence in Galerkin finite element methods |
| title_sort | superconvergence in galerkin finite element methods |
| topic | Elliptisches Randwertproblem (DE-588)4193399-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Galerkin-Methode (DE-588)4155831-5 gnd Konvergenz (DE-588)4032326-2 gnd |
| topic_facet | Elliptisches Randwertproblem Finite-Elemente-Methode Galerkin-Methode Konvergenz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006774512&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT wahlbinlarsb superconvergenceingalerkinfiniteelementmethods |
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Teilbibliothek Mathematik & Informatik
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0102 MAT 001z 2001 B 999-1605 Lageplan |
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