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Accuracy Verification Methods (Record no. 404025)

MARC details
000 -Маркер записи
Контрольное поле постоянной длины 08018nam a22005415i 4500
001 - Контрольный номер
Контрольное поле vtls000546336
005 - Дата корректировки
Контрольное поле 20210922083606.0
007 - Кодируемые данные (физ. описан.)
Контрольное поле постоянной длины cr nn 008mamaa
008 - Кодируемые данные
Контрольное поле постоянной длины 160915s2014 ne | s |||| 0|eng d
020 ## - Индекс ISBN
ISBN 9789400775817
-- 978-94-007-7581-7
024 7# - Прочие стандартные номера
Стандартный номер 10.1007/978-94-007-7581-7
Источник номера doi
035 ## - Системный контрольный номер
Системный контрольный номер to000546336
040 ## - Источник каталогиз.
Служба первич. каталог. Springer
Служба, преобразующая запись Springer
Организация, изменившая запись RU-ToGU
050 #4 - Расстановочный код библ. Конгресса
Классификационный индекс QA297-299.4
072 #7 - Код предметной/темат. категории
Код предметной/темат. категории UYA
Источник кода bicssc
072 #7 - Код предметной/темат. категории
Код предметной/темат. категории COM051300
Источник кода bisacsh
082 04 - Индекс Дьюи
Индекс Дьюи 518
Номер издания 23
100 1# - Автор
Автор Mali, Olli.
Роль лиц author.
9 (RLIN) 455306
245 10 - Заглавие
Заглавие Accuracy Verification Methods
Физический носитель electronic resource
Продолж. заглавия Theory and Algorithms /
Ответственность by Olli Mali, Pekka Neittaanmäki, Sergey Repin.
260 ## - Выходные данные
Место издания Dordrecht :
Издательство Springer Netherlands :
-- Imprint: Springer,
Дата издания 2014.
300 ## - Физическое описание
Объем XIII, 355 p. 75 illus.
Иллюстрации/тип воспроизводства online resource.
336 ## - Тип содержимого
Тип содержимого text
Content type code txt
Source rdacontent
337 ## - Средство доступа
Средство доступа computer
Media type code c
Source rdamedia
338 ## - Тип носителя
Тип носителя online resource
Carrier type code cr
Source rdacarrier
490 1# - Серия
Заглавие серии Computational Methods in Applied Sciences,
ISSN серии 1871-3033 ;
№ тома 32
505 0# - Примечание о содержании
Содержание 1 Errors Arising In Computer Simulation Methods -- 1.1 General scheme -- 1.2 Errors of mathematical models -- 1.3 Approximation errors -- 1.4 Numerical errors -- 2 Error Indicators -- 2.1 Error indicators and adaptive numerical methods -- 2.1.1 Error indicators for FEM solutions -- 2.1.2 Accuracy of error indicators -- 2.2 Error indicators for the energy norm -- 2.2.1 Error indicators based on interpolation estimates -- 2.2.2 Error indicators based on approximation of the error functional -- 2.2.3 Error indicators of the Runge type -- 2.3 Error indicators for goal-oriented quantities -- 2.3.1 Error indicators relying on the superconvergence of averaged fluxes in the primal and adjoint problems -- 2.3.2 Error indicators using the superconvergence of approximations in the primal problem -- 2.3.3 Error indicators based on partial equilibration of fluxes in the original problem -- 3 Guaranteed Error Bounds I -- 3.1 Ordinary differential equations -- 3.1.1 Derivation of guaranteed error bounds -- 3.1.2 Computation of error bounds -- 3.2 Partial differential equations -- 3.2.1 Maximal deviation from the exact solution -- 3.2.2 Minimal deviation from the exact solution -- 3.2.3 Particular cases -- 3.2.4 Problems with mixed boundary conditions -- 3.2.5 Estimates of global constants entering the majorant -- 3.2.6 Error majorants based on Poincar´e inequalities -- 3.2.7 Estimates with partially equilibrated fluxes -- 3.3 Error control algorithms -- 3.3.1 Global minimization of the majorant -- 3.3.2 Getting an error bound by local procedures -- 3.4 Indicators based on error majorants -- 3.5 Applications to adaptive methods -- 3.6 Combined (primal-dual) error norms and the majorant -- 4 Guaranteed Error Bounds II -- 4.1 Linear elasticity -- 4.1.1 Introduction -- 4.1.2 Euler–Bernoulli beam -- 4.1.3 The Kirchhoff–Love arch model -- 4.1.4 The Kirchhoff–Love plate -- 4.1.5 The Reissner–Mindlin plate -- 4.1.6 3D linear elasticity -- 4.1.7 The plane stress model -- 4.1.8 The plane strain model -- 4.2 The Stokes Problem -- 4.2.1 Divergence-free approximations -- 4.2.2 Approximations with nonzero divergence -- 4.2.3 Stokes problem in rotating system -- 4.3 A simple Maxwell type problem -- 4.3.1 Estimates of deviations from exact solutions -- 4.3.2 Numerical examples -- 4.4 Generalizations -- 4.4.1 Error majorant -- 4.4.2 Error minorant -- 5 Errors Generated By Uncertain Data -- 5.1 Mathematical models with incompletely known data -- 5.2 The accuracy limit -- 5.3 Estimates of the worst and best case scenario errors -- 5.4 Two-sided bounds of the radius of the solution set -- 5.5 Computable estimates of the radius of the solution set -- 5.5.1 Using the majorant -- 5.5.2 Using a reference solution -- 5.5.3 An advanced lower bound -- 5.6 Multiple sources of indeterminacy -- 5.6.1 Incompletely known right-hand side -- 5.6.2 The reaction diffusion problem -- 5.7 Error indication and indeterminate data -- 5.8 Linear elasticity with incompletely known Poisson ratio -- 5.8.1 Sensitivity of the energy functional -- 5.8.2 Example: axisymmetric model -- 6 Overview Of Other Results And Open Problems -- 6.1 Error estimates for approximations violating conformity -- 6.2 Linear elliptic equations -- 6.3 Time-dependent problems -- 6.4 Optimal control and inverse problems -- 6.5 Nonlinear boundary value problems -- 6.5.1 Variational inequalities -- 6.5.2 Elastoplasticity -- 6.5.3 Problems with power growth energy functionals -- 6.6 Modeling errors -- 6.7 Error bounds for iteration methods -- 6.7.1 General iteration algorithm -- 6.7.2 A priori estimates of errors -- 6.7.3 A posteriori estimates of errors -- 6.7.4 Advanced forms of error bounds -- 6.7.5 Systems of linear simultaneous equations -- 6.7.6 Ordinary differential equations -- 6.8 Roundoff errors -- 6.9 Open problems -- A Mathematical Background -- A.1 Vectors and tensors -- A.2 Spaces of functions -- A.2.1 Lebesgue and Sobolev spaces -- A.2.2 Boundary traces -- A.2.3 Linear functionals -- A.3 Inequalities -- A.3.1 The Hölder inequality -- A.3.2 The Poincaré and Friedrichs inequalities -- A.3.3 Korn’s inequality -- A.3.4 LBB inequality -- A.4 Convex functionals -- B Boundary Value Problems -- B.1 Generalized solutions of boundary value problems -- B.2 Variational statements of elliptic boundary value problems -- B.3 Saddle point statements of elliptic boundary value problems -- B.3.1 Introduction to the theory of saddle points -- B.3.2 Saddle point statements of linear elliptic problems -- B.3.3 Saddle point statements of nonlinear variational problems -- B.4 Numerical methods -- B.4.1 Finite difference methods -- B.4.2 Variational difference methods -- B.4.3 Petrov–Galerkin methods -- B.4.4 Mixed finite element methods -- B.4.5 Trefftz methods -- B.4.6 Finite volume methods -- B.4.7 Discontinuous Galerkin methods -- B.4.8 Fictitious domain methods -- C A Priori Verification Of Accuracy -- C.1 Projection error estimate -- C.2 Interpolation theory in Sobolev spaces -- C.3 A priori convergence rate estimates -- C.4 A priori error estimates for mixed FEM -- References -- Notation --  Index.
520 ## - Аннотация
Аннотация The importance of accuracy verification methods was understood at the very beginning of the development of numerical analysis. Recent decades have seen a rapid growth of results related to adaptive numerical methods and a posteriori estimates. However, in this important area there often exists a noticeable gap between mathematicians creating the theory and researchers developing applied algorithms that could be used in engineering and scientific computations for guaranteed and efficient error control.   The goals of the book are to (1) give a transparent explanation of the underlying mathematical theory in a style accessible not only to advanced numerical analysts but also to engineers and students; (2) present detailed step-by-step algorithms that follow from a theory; (3) discuss their advantages and drawbacks, areas of applicability, give recommendations and examples.
650 #0 - Тематические рубрики
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9 (RLIN) 155490
650 #0 - Тематические рубрики
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650 #0 - Тематические рубрики
Основная рубрика Numerical analysis.
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650 #0 - Тематические рубрики
Основная рубрика engineering.
9 (RLIN) 224332
650 14 - Тематические рубрики
Основная рубрика Computer Science.
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650 24 - Тематические рубрики
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650 24 - Тематические рубрики
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650 24 - Тематические рубрики
Основная рубрика Numerical Analysis.
9 (RLIN) 566289
650 24 - Тематические рубрики
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9 (RLIN) 410438
650 24 - Тематические рубрики
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700 1# - Другие авторы
Другие авторы Neittaanmäki, Pekka.
Роль лиц author.
9 (RLIN) 81646
700 1# - Другие авторы
Другие авторы Repin, Sergey.
Роль лиц author.
9 (RLIN) 455307
710 2# - Другие организации
Организация/юрисдикция SpringerLink (Online service)
9 (RLIN) 143950
773 0# - Источник информации
Название источника Springer eBooks
830 #0 - Заголовок добавочной библ.записи на серию — унифицированное заглавие
Унифицированное заглавие Computational Methods in Applied Sciences,
9 (RLIN) 311339
856 40 - Электронный адрес документа
URL <a href="http://dx.doi.org/10.1007/978-94-007-7581-7">http://dx.doi.org/10.1007/978-94-007-7581-7</a>
912 ## - Coursera for Campus: онлайн курсы для ТГУ
Coursera for Campus: онлайн курсы для ТГУ ZDB-2-ENG
999 ## - Системные контрольные номера (Koha)
biblionumber (Koha) 404025

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