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Error Estimates for Advanced Galerkin Methods

  • Marcus Olavi Rüter
Book

Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 88)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Marcus Olavi Rüter
    Pages 1-14
  3. Marcus Olavi Rüter
    Pages 15-54
  4. Marcus Olavi Rüter
    Pages 55-74
  5. Marcus Olavi Rüter
    Pages 75-148
  6. Marcus Olavi Rüter
    Pages 149-170
  7. Marcus Olavi Rüter
    Pages 171-278
  8. Marcus Olavi Rüter
    Pages 353-420
  9. Back Matter
    Pages 421-496

About this book

Introduction

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.

Keywords

Elastic Fracture Mechanics Enhanced-strain Error Estimation Finite Element Method Reproducing Kernel Particle Method Goal-oriented Error Estimation Finite and Linearized Hyperelasticity Discretization and Integration Error

Authors and affiliations

  • Marcus Olavi Rüter
    • 1
  1. 1.Department of Civil and Environmental EngineeringUniversity of CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-06173-9
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-030-06172-2
  • Online ISBN 978-3-030-06173-9
  • Series Print ISSN 1613-7736
  • Series Online ISSN 1860-0816
  • Buy this book on publisher's site