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Error Estimates for Advanced Galerkin Methods

  • Book
  • © 2019

Overview

Authors:
  1. Marcus Olavi Rüter

    1. Department of Civil and Environmental Engineering, University of California, Los Angeles, USA

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  • Sheds light on various aspects of the error estimation procedures, as well as on nonlinear problems within the framework of finite hyperelasticity
  • Showcases comparative numerical examples for problems in elastic fracture mechanics
  • Provides a comprehensive compendium, from continuum mechanics, boundary value problems and their discretization, as well as numerical integration into error estimation procedures

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Introduction

    • Marcus Olavi Rüter
    Pages 1-14

  3. Newtonian and Eshelbian Mechanics

    • Marcus Olavi Rüter
    Pages 15-54

  4. Boundary Value Problems

    • Marcus Olavi Rüter
    Pages 55-74

  5. Galerkin Methods

    • Marcus Olavi Rüter
    Pages 75-148

  6. Numerical Integration

    • Marcus Olavi Rüter
    Pages 149-170

  7. Energy Norm A Posteriori Error Estimates

    • Marcus Olavi Rüter
    Pages 171-278

  8. Goal-oriented A Posteriori Error Estimates in Linearized Elasticity

    • Marcus Olavi Rüter
    Pages 279-318

  9. Goal-oriented A Posteriori Error Estimates in Finite Hyperelasticity

    • Marcus Olavi Rüter
    Pages 319-352

  10. Numerical Examples

    • Marcus Olavi Rüter
    Pages 353-420

  11. Back Matter

    Pages 421-496
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Civil and Environmental Engineering, University of California, Los Angeles, USA

    Marcus Olavi Rüter

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