Skip to main content
SpringerLink
Log in

Comparison of Adaptive Non-symmetric and Three-Field FVM-BEM Coupling

  • Conference paper
  • First Online:
Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems (FVCA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 200))

Included in the following conference series:

  • 1326 Accesses

Abstract

The prototype for flow and transport in porous media in an interior domain is coupled to the Laplace equation on the complement, an unbounded domain. We approximate the solution of this interface problem either by the non-symmetric or the three-field coupling of the Finite Volume Method (FVM) and the Boundary Element Method (BEM). For these two coupling methods we introduce (semi-) robust a posteriori error estimators and use them in an adaptive algorithm to improve the convergence. Numerical experiments compare these two adaptive methods in terms of effectivity index, errors and mesh refinement.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Erath, C.: Coupling of the finite volume element method and the boundary element method: an a priori convergence result. SIAM J. Numer. Anal. 50(2), 574–594 (2012). doi:10.1137/110833944

    Article  MathSciNet  MATH  Google Scholar 

  2. Erath, C.: A posteriori error estimates and adaptive mesh refinement for the coupling of the finite volume method and the boundary element method. SIAM J. Numer. Anal. 51(3), 1777–1804 (2013). doi:10.1137/110854771

    Article  MathSciNet  MATH  Google Scholar 

  3. Erath, C., Of, G., Sayas, F.J.: A non-symmetric coupling of the finite volume method and the boundary element method. Numer. Math. 135(3), 895–922 (2017). doi:10.1007/s00211-016-0820-3

    Article  MathSciNet  MATH  Google Scholar 

  4. Erath, C., Schorr, R.: An adaptive non-symmetric finite volume and boundary element coupling method for a fluid mechanics interface problem. in press, SIAM J. Sci. Comput. (2017)

    Google Scholar 

Download references

Acknowledgements

The work of the second author is supported by the Excellence Initiative of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt.

Author information

Authors and Affiliations

  1. TU Darmstadt, Department of Mathematics, Dolivostraße 15, 64293, Darmstadt, Germany

    Christoph Erath

  2. TU Darmstadt, Department of Mathematics/GSC CE, Dolivostraße 15, 64293, Darmstadt, Germany

    Robert Schorr

Authors
  1. Christoph Erath
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Schorr
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christoph Erath .

Editor information

Editors and Affiliations

  1. Equipe RAPSODI, Inria Lille - Nord Europe, Villeneuve-d’Ascq, France

    Clément Cancès

  2. Commissariat à l'énergie atomique et aux énergies alternatives, Centre de Saclay, Gif-sur-Yvette, France

    Pascal Omnes

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Erath, C., Schorr, R. (2017). Comparison of Adaptive Non-symmetric and Three-Field FVM-BEM Coupling. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_36

Download citation

Publish with us

Policies and ethics

Search

Navigation