© 2020

Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

FVCA 9, Bergen, Norway, June 2020

  • Robert Klöfkorn
  • Eirik Keilegavlen
  • Florin A. Radu
  • Jürgen Fuhrmann


  • Comprehensive overview of the state of the art

  • Both theoretical and applied aspects are covered

  • Authors are leading researchers from the community

Conference proceedings FVCA 2020

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 323)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Invited Contributions

    1. Front Matter
      Pages 1-1
    2. Alessio Fumagalli, Anna Scotti
      Pages 55-73
    3. Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet, Hélène Mathis
      Pages 75-90
  3. Theoretical Aspects

    1. Front Matter
      Pages 91-91
    2. T. Gallouët, R. Herbin, J.-C. Latché, Y. Nasseri
      Pages 123-131
    3. Clément Cancès, Claire Chainais Hillairet, Jürgen Fuhrmann, Benoît Gaudeul
      Pages 163-171
    4. Clément Cancès, Benoît Gaudeul
      Pages 183-191
    5. Andrea Natale, Gabriele Todeschi
      Pages 193-201
    6. Jakub W. Both, Jan M. Nordbotten, Florin A. Radu
      Pages 203-211

About these proceedings


The proceedings of the 9th conference on "Finite Volumes for Complex Applications" (Bergen, June 2020) are structured in two volumes. The first volume collects 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. Topics covered include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. Altogether, a rather comprehensive overview is given on the state of the art in the field. The properties of the methods considered in the conference give them distinguished advantages for a number of applications. These include fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory, carbon capture utilization and storage, geothermal energy and further topics. The second volume covers reviewed contributions reporting successful applications of finite volume and related methods in these fields. 

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. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability, making the finite volume methods 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. 

The book is a valuable resource for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.


65-06, 65Mxx, 65Nxx, 76xx, 78xx,85-08, 86-08, 92-08 finite volume schemes conservation and balance laws numerical analysis high performance computing incompressible flows drift-diffusion equations entropy methods shallow water equations open source software cut-cell methods fractured porous media

Editors and affiliations

  • Robert Klöfkorn
    • 1
  • Eirik Keilegavlen
    • 2
  • Florin A. Radu
    • 3
  • Jürgen Fuhrmann
    • 4
  1. 1.NORCE Norwegian Research Centre ASBergenNorway
  2. 2.Department of MathematicsUniversity of BergenBergenNorway
  3. 3.Department of MathematicsUniversity of BergenBergenNorway
  4. 4.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

Bibliographic information