Approximation on a rectangular grid: with applications to finite element methods and other problems
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch Russisch |
| Veröffentlicht: |
Alphen aan den Rijn u.a.
Sijthoff & Noordhoff
1979
|
| Schriftenreihe: | Monographs and textbooks on mechanics of solids and fluids / Mechanics: Analysis
4 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 224 S. |
| ISBN: | 9028600086 |
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| 240 | 1 | 0 | |a Approksimacija na kubičeskoj setke |
| 245 | 1 | 0 | |a Approximation on a rectangular grid |b with applications to finite element methods and other problems |c S. G. Mikhlin |
| 264 | 1 | |a Alphen aan den Rijn u.a. |b Sijthoff & Noordhoff |c 1979 | |
| 300 | |a XI, 224 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs and textbooks on mechanics of solids and fluids / Mechanics: Analysis |v 4 | |
| 650 | 4 | |a Approximation, Théorie de l' | |
| 650 | 4 | |a Problèmes aux limites | |
| 650 | 4 | |a Treillis, Théorie des | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Lattice theory | |
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| 810 | 2 | |a Mechanics: Analysis |t Monographs and textbooks on mechanics of solids and fluids |v 4 |w (DE-604)BV001891479 |9 4 | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 674f 2001 A 25083 |
|---|---|
| DE-BY-TUM_katkey | 498043 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010438778 |
| _version_ | 1821936890633256960 |
| adam_text | IX
TABLE OF CONTENTS
CHAPTER I: THE PRIMITIVE FUNCTIONS 1
§1. The Variational Difference Method 1
§2. An Example 3
§3. The Basic Properties of Variational Difference Matrices .. 9
§4. Primitive Functions and Coordinate Functions 12
§5. Interpolatory Properties of Primitive Systems of Functions 18
CHAPTER II: COMPLETENESS AND FUNDAMENTAL COMPLETENESS CONDITIONS 19
§1. Approximation of Smooth Functions 19
§2. Extensions of Functions 23
§3. Completeness in Sobolev Spaces 29
§4. On the Minimum Number of Primitive Functions 31
§5. The Necessity of the Fundamental Completeness Conditions 32
§6. One Dimensional Primitive Systems 35
§7. Primitive Systems of Higher Dimensions with Zero Degree .. 39
§8. Primitive Systems with m ~ s = 2 44
§9. Product Primitive Systems 49
CHAPTER III: ORDER OF APPROXIMATION 52
§1. Order of Approximation using the Uniform Norm 52
§2. On the Averaging of Functions 56
§3. The Order of Approximation for Sobolev Spaces 59
§4. Estimation of the Constants for the Simplest Case .... 61
§5. Approximation Using Product Primitive Functions 64
§6. Strengthened Fundamental Completeness Conditions .... 66
§7. Some General Considerations 70
§8. A More General Class of Primitive Systems 72
x Table of Contents
CHAPTER IV: PRIMITIVE FUNCTIONS WITH WIDE SUPPORT 73
§1. Definitions 73
§2. Fundamental Completeness Conditions for One Dimensional
Systems 75
§3. Example: The Parabolic Approximation 77
§4. Fundamental Completeness Conditions for Systems of
Arbitrary Dimension 79
CHAPTER V: APPROXIMATION IN ONE DIMENSIONAL DEGENERATE NORMS 81
§1. The Formulation of the Problem 81
§2. On the Completeness of Coordinate Systems Which are
Complete with Respect to Non Degenerate Norms 83
§3. Equations of Second Order with Weak Degeneracy 87
§4. The Case 1 ^ a 2 91
§5. Properties of the Solution 93
§6. Improved Estimates 96
§7. The Case a 2
§8. More General Equations 99
§9. Approximation in L 104
§10. Other Boundary Conditions 105
CHAPTER VI: SOME DEGENERATE TWO DIMENSIONAL NORMS 107
§1. Approximations for Radially Symmetric Grids 107
§2. Estimation of the First Integral 109
§3. Estimation of the Second Integral 113
§4. The Class CC2 a) 116
§5. Approximation on L and C 117
§6. Degenerate Second Order Elliptic Equations 118
CHAPTER VII: APPROXIMATION OF EIGENVALUES 121
§1. On the Order of the Largest Approximate Eigenvalue.
Formulation of the Problem 121
§2. The Rayleigh Ritz Process 123
§3. One Dimensional Variational Difference Processes .. .. 123
§4. The Case of Several Variables 127
§5. Error Estimate for Fixed Eigenvalues 131
CHAPTER VIII: CONSTRUCTION OF VARIATIONAL DIFFERENCE EQUATIONS 135
§1. First Boundary Value Problems: Equations with Constant
Coefficients on a Cube 135
§2. First Boundary Value Problems: Equations with Variable
Coefficients on a Cube 138
§3. First Boundary Value Problems: Natural Boundary
Conditions 139
§4. First Boundary Value Problems: Approximation of the
Boundary Conditions 141
Table of Contents XI
§5. Variational Difference Methods on an Axial Symmetric Grid 145
§6. Variational Difference Schemes Containing a Boundary
Layer: The One Dimensional Situation 147
§7. Variational Difference Schemes Containing a Boundary
Layer: The Multidimensional Situation 152
§8. Non Self Adjoint Problems 154
CHAPTER IX: ERROR ESTIMATES FOR THE VARIATIONAL DIFFERENCE METHOD .. .. 157
§1. On the Stability of Numerical Processes 157
§2. The Stability of Variational Difference Processes The
One Dimensional Problem 160
§3. The Stability of Variational Difference Processes
Multi Dimensional Problems 165
§4. The Stability of Variational Difference Processes
Eigenvalue Problems 170
§5. On the Condition Number of the Variational Difference
Matrix 171
§6. The Case of Arbitrary Domains and Arbitrary Boundary
Conditions 173
§7. Numerical Example A Degenerate Second Order Ordinary
Differential Equation 174
CHAPTER X: THE EULER MACLAURIN SUM FORMULA 181
§1. A New Derivation of the Euler Maclaurin Sum Formula .. 181
§2. A Related Euler Maclaurin Sum Formula 184
§3. An Euler Maclaurin Sum Formula for the Multidimensional
Cube 185
§4. Integration Over a Ball 18 8
CHAPTER XI: ON INTEGRAL EQUATIONS 192
§1. Approximation of the Kernel and Resolvent 193
§2. The Accuracy of the Approximation 196
§3. Rounding Error Accumulation Absolute Estimates .. .. 198
§4. Rounding Error Accumulation Probabilistic Estimates .. 202
§5. Integral Equations Which Can be Solved by Iteration .. 203
§6. Some Additional Notes 206
|7. Equations with Weak Singularities 207
§8. Integral Equations of Heat Conduction 208
REFERENCES 215
INDEX 220
|
| any_adam_object | 1 |
| author | Michlin, Solomon G. 1908-1990 |
| author_GND | (DE-588)172258243 |
| author_facet | Michlin, Solomon G. 1908-1990 |
| author_role | aut |
| author_sort | Michlin, Solomon G. 1908-1990 |
| author_variant | s g m sg sgm |
| building | Verbundindex |
| bvnumber | BV003714794 |
| callnumber-first | Q - Science |
| callnumber-label | QA379 |
| callnumber-raw | QA379 |
| callnumber-search | QA379 |
| callnumber-sort | QA 3379 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 910 |
| ctrlnum | (OCoLC)5758133 (DE-599)BVBBV003714794 |
| dewey-full | 511.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.4 |
| dewey-search | 511.4 |
| dewey-sort | 3511.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003714794 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T08:09:05Z |
| institution | BVB |
| isbn | 9028600086 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002364610 |
| oclc_num | 5758133 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-824 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-824 |
| physical | XI, 224 S. |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | Sijthoff & Noordhoff |
| record_format | marc |
| series2 | Monographs and textbooks on mechanics of solids and fluids / Mechanics: Analysis |
| spellingShingle | Michlin, Solomon G. 1908-1990 Approximation on a rectangular grid with applications to finite element methods and other problems Approximation, Théorie de l' Problèmes aux limites Treillis, Théorie des Approximation theory Boundary value problems Lattice theory Funktion (DE-588)4195664-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4195664-3 (DE-588)4017233-8 |
| title | Approximation on a rectangular grid with applications to finite element methods and other problems |
| title_alt | Approksimacija na kubičeskoj setke |
| title_auth | Approximation on a rectangular grid with applications to finite element methods and other problems |
| title_exact_search | Approximation on a rectangular grid with applications to finite element methods and other problems |
| title_full | Approximation on a rectangular grid with applications to finite element methods and other problems S. G. Mikhlin |
| title_fullStr | Approximation on a rectangular grid with applications to finite element methods and other problems S. G. Mikhlin |
| title_full_unstemmed | Approximation on a rectangular grid with applications to finite element methods and other problems S. G. Mikhlin |
| title_short | Approximation on a rectangular grid |
| title_sort | approximation on a rectangular grid with applications to finite element methods and other problems |
| title_sub | with applications to finite element methods and other problems |
| topic | Approximation, Théorie de l' Problèmes aux limites Treillis, Théorie des Approximation theory Boundary value problems Lattice theory Funktion (DE-588)4195664-3 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Approximation, Théorie de l' Problèmes aux limites Treillis, Théorie des Approximation theory Boundary value problems Lattice theory Funktion Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001891479 |
| work_keys_str_mv | AT michlinsolomong approksimacijanakubiceskojsetke AT michlinsolomong approximationonarectangulargridwithapplicationstofiniteelementmethodsandotherproblems |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 674f 2001 A 25083 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |