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Meshfree Methods for Partial Differential Equations VIII

  • Michael Griebel
  • Marc Alexander Schweitzer

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 115)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Patrick Diehl, Michael Bußler, Dirk Pflüger, Steffen Frey, Thomas Ertl, Filip Sadlo et al.
    Pages 17-34
  3. Adeleke O. Bankole, Michael Dumbser, Armin Iske, Thomas Rung
    Pages 35-52
  4. Yanping Lian, Gregory J. Wagner, Wing Kam Liu
    Pages 53-66
  5. Alexander A. Lukyanov, Cornelis Vuik
    Pages 67-84
  6. Donald L. Brown, Dietmar Gallistl, Daniel Peterseim
    Pages 85-115
  7. Robert Schaback
    Pages 117-143
  8. Marc Alexander Schweitzer, Albert Ziegenhagel
    Pages 199-208
  9. Back Matter
    Pages 233-240

About these proceedings

Introduction

There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods have a number of advantageous features that are especially attractive when dealing with multiscale phenomena: A-priori knowledge about the solution’s particular local behavior can easily be introduced into the meshfree approximation space, and coarse scale approximations can be seamlessly refined by adding fine scale information. However, the implementation of meshfree methods and their parallelization also requires special attention, for instance with respect to numerical integration.

Keywords

meshfree methods generalized finite elements fracture mechanics radial basis functions smoothed particle hydrodynamics

Editors and affiliations

  • Michael Griebel
    • 1
  • Marc Alexander Schweitzer
    • 2
  1. 1.Institut für Numerische SimulationUniversität BonnBonnGermany
  2. 2.Institut für Numerische SimulationUniversität BonnBonnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-51954-8
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-51953-1
  • Online ISBN 978-3-319-51954-8
  • Series Print ISSN 1439-7358
  • Series Online ISSN 2197-7100
  • Buy this book on publisher's site