ENGLISH

Error Estimates for Advanced Galerkin Methods

By Marcus Olavi Rüter

Book information

Publisher
Springer International Publishing
Year
2019
ISBN
978-3-030-06172-2, 978-3-030-06173-9
Language
english
Format
PDF
Filesize
23 MB (23671354 bytes)
Series
Lecture Notes in Applied and Computational Mechanics 88
Edition
1st ed. 2019
Pages
XIV, 496\505
Time added
2020-02-08 04:41:00
Engineering; Computational Science and Engineering

Description

This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures. Front Matter ....Pages i-xiv Introduction (Marcus Olavi Rüter)....Pages 1-14 Newtonian and Eshelbian Mechanics (Marcus Olavi Rüter)....Pages 15-54 Boundary Value Problems (Marcus Olavi Rüter)....Pages 55-74 Galerkin Methods (Marcus Olavi Rüter)....Pages 75-148 Numerical Integration (Marcus Olavi Rüter)....Pages 149-170 Energy Norm A Posteriori Error Estimates (Marcus Olavi Rüter)....Pages 171-278 Goal-oriented A Posteriori Error Estimates in Linearized Elasticity (Marcus Olavi Rüter)....Pages 279-318 Goal-oriented A Posteriori Error Estimates in Finite Hyperelasticity (Marcus Olavi Rüter)....Pages 319-352 Numerical Examples (Marcus Olavi Rüter)....Pages 353-420 Back Matter ....Pages 421-496

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