Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

FVCA 7, Berlin, June 2014

  • Jürgen Fuhrmann
  • Mario Ohlberger
  • Christian Rohde
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 77)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Invited Papers

    1. Front Matter
      Pages 1-1
    2. Ann Almgren, John Bell, Andrew Nonaka, Michael Zingale
      Pages 3-15
  3. Theoretical Aspects

    1. Front Matter
      Pages 55-55
    2. Remi Abgrall, Luca Arpaia, Mario Ricchiuto
      Pages 57-65
    3. Yahya Alnashri, Jerome Droniou
      Pages 67-75
    4. M. J. H. Anthonissen, J. H. M. ten Thije Boonkkamp
      Pages 77-85
    5. Fabrice Babik, Jean-Claude Latché, Bruno Piar, Khaled Saleh
      Pages 87-95
    6. Florent Berthelin, Thierry Goudon, Sebastian Minjeaud
      Pages 97-105
    7. J. H. M. ten Thije Boonkkamp, M. J. H. Anthonissen
      Pages 117-125
    8. Christian Brennecke, Alexander Linke, Christian Merdon, Joachim Schöberl
      Pages 159-167
    9. Jens Brouwer, Julius Reiss, Jörn Sesterhenn
      Pages 169-176
    10. Fabian Brunner, Florian Frank, Peter Knabner
      Pages 177-185

About these proceedings

Introduction

The first volume of the proceedings of the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) covers topics that include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers, as well as the reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods. Altogether, a rather comprehensive overview is given of the state of the art in the field.

The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications.

Researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations will find this volume useful, as will engineers working in numerical modeling and simulations.

Keywords

65-06, 65Mxx, 65Nxx, 76xx, 78xx, 85-08, 86-08, 92-08 compatible discretizations convergence analysis finite volume methods numerical methods partial differential equations

Editors and affiliations

  • Jürgen Fuhrmann
    • 1
  • Mario Ohlberger
    • 2
  • Christian Rohde
    • 3
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Institute Comp. Applied MathematicsUniversity of Münster Center for Nonlinear Sciences (CeNoS )MünsterGermany
  3. 3.Inst. Appl. Analysis and Num. SimulationUniversity of StuttgartStuttgartGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-05684-5
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-05683-8
  • Online ISBN 978-3-319-05684-5
  • Series Print ISSN 2194-1009
  • Series Online ISSN 2194-1017
  • About this book