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Comparison of Two Couplings of the Finite Volume Method and the Boundary Element Method

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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

Abstract

In many fluid dynamics problems the boundary conditions may be unknown, or the domain may be unbounded. Also mass conservation and stability with respect to dominating convection is substantial. Therefore, we test two coupling methods to address these issues on the prototype of a flow and transport problem. More precisely, we couple the vertex-centered and the cell-centered finite volume method with the boundary element method, FVM-BEM and CFVM-BEM, respectively. Also robust refinement indicators are considered which allow us to steer an adaptive mesh-refinement algorithm to treat efficiently problems with singularities or boundary/internal layers—shown on two examples.

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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)

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  3. 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)

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  4. Erath, C., Praetorius, D.: A posteriori error estimate and adaptive mesh refinement for the cell-centered finite volume method for elliptic boundary value problems. SIAM J. Numer. Anal. 47(1), 109–135 (2008)

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Authors and Affiliations

  1. Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Vienna, 1090, Austria

    Christoph Erath

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  1. Christoph Erath
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Correspondence to Christoph Erath .

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Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    JĂĽrgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of MĂĽnster Center for Nonlinear Sciences (CeNoS ), MĂĽnster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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Erath, C. (2014). Comparison of Two Couplings of the Finite Volume Method and the Boundary Element Method. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_24

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