A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical ApproximationsSpringer Science & Business Media, 19 de nov. de 2004 - 302 páginas 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. |
Conteúdo
IV | 1 |
VI | 5 |
VII | 7 |
VIII | 16 |
IX | 20 |
X | 25 |
XI | 29 |
XII | 36 |
XXVII | 127 |
XXVIII | 143 |
XXIX | 160 |
XXX | 169 |
XXXI | 173 |
XXXII | 176 |
XXXIII | 182 |
XXXIV | 193 |
XIII | 47 |
XIV | 50 |
XV | 52 |
XVI | 56 |
XVII | 57 |
XVIII | 59 |
XIX | 61 |
XX | 67 |
XXI | 68 |
XXII | 91 |
XXIII | 100 |
XXIV | 106 |
XXV | 112 |
XXVI | 119 |
XXXV | 203 |
XXXVI | 209 |
XXXVII | 219 |
XXXVIII | 226 |
XXXIX | 235 |
XL | 237 |
XLI | 243 |
XLII | 248 |
XLIII | 255 |
XLIV | 262 |
XLV | 271 |
287 | |
301 | |
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A Posteriori Error Analysis Via Duality Theory: With Applications in ... Weimin Han Visualização parcial - 2006 |
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Termos e frases comuns
adapted mesh approximation assume assumption auxiliary function bilinear form boundary condition boundary value problem coefficient conjugate function consider constant convergence convex functions corner domain defined denote derive a posteriori dual problem duality theory ED(u energy function error bound Example finite element method finite element solution g₁ Gâteaux derivative gradient recovery type H¹(N idealized Kačanov iterates Kačanov method L²(N Lax-Milgram Lemma Lemma linear problem linearized elasticity Lipschitz continuous Lipschitz domain mathematical minimization problem nodes nonlinear problem normed space numerical results obstacle problem obtain posteriori error analysis posteriori error estimates residual type estimator results based sequence Sobolev Sobolev spaces solving subset triangle uniform mesh unique solution upper bound variational inequality Vuol² Vv dx weak formulation г₁ მი
Referências a este livro
Theoretical Numerical Analysis: A Functional Analysis Framework Kendall Atkinson,Weimin Han Visualização parcial - 2007 |
Analysis and Approximation of Contact Problems with Adhesion or Damage Mircea Sofonea,Weimin Han,Meir Shillor Visualização parcial - 2005 |