A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations

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Springer Science & Business Media, 2005 - Mathematics - 302 pages
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This work provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear var- tional problems. An error estimate is called a posteriori if the computed solution is used in assessing its accuracy. A posteriori error estimation is central to m- suring, controlling and minimizing errors in modeling and numerical appr- imations. In this book, the main mathematical tool for the developments of a posteriori error estimates is the duality theory of convex analysis, documented in the well-known book by Ekeland and Temam ([49]). The duality theory has been found useful in mathematical programming, mechanics, numerical analysis, etc. The book is divided into six chapters. The first chapter reviews some basic notions and results from functional analysis, boundary value problems, elliptic variational inequalities, and finite element approximations. The most relevant part of the duality theory and convex analysis is briefly reviewed in Chapter 2.
  

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Contents

IV
1
V
5
VI
7
VII
16
VIII
20
IX
25
X
29
XI
36
XXVI
127
XXVII
143
XXVIII
160
XXIX
169
XXX
173
XXXI
176
XXXII
182
XXXIII
193

XII
47
XIII
50
XIV
52
XV
56
XVI
57
XVII
59
XVIII
61
XIX
67
XX
68
XXI
91
XXII
100
XXIII
106
XXIV
112
XXV
119
XXXIV
203
XXXV
209
XXXVI
219
XXXVII
226
XXXVIII
235
XXXIX
237
XL
243
XLI
248
XLII
255
XLIII
262
XLIV
271
XLV
287
XLVI
301
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