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A Domain-Based Multinumeric Method for the Steady-State Convection-Diffusion Equation

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Domain Decomposition Methods in Science and Engineering XXI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 98))

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Abstract

A multinumeric approach is formulated. The computational domain is partitioned into several subdomains. On each subdomain, either a discontinuous Galerkin method is used or a cell-centered finite volume is used. Both methods are locally mass conservatives and therefore well-suited for modeling porous media flows. Convergence of the method is obtained by deriving a priori error estimates.

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References

  1. Brezzi, F., Johnson, C.: On the coupling of boundary integral and finite element methods. Calcolo 16, 189–201 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chidyagwai, P., Mishev, I., Riviere, B.: On the coupling of finite volume and discontinuous Galerkin method for elliptic problems. J. Comput. Appl. Math. 231, 2193–2204 (2011)

    Article  MathSciNet  Google Scholar 

  3. Eymard, R., Gallouët, T., Herbin, R.: Finite volume methods. In: Handbook of Numerical Analysis, vol. VII. North-Holland, Amsterdam (2000)

    Google Scholar 

  4. Forsyth, P., Sammon, P.: Quadratic convergence for cell-centered grids. Appl. Numer. Math. 4, 377–394 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  5. Johnson, C., Nédélec, J.: On the coupling of boundary integral and finite element methods. Math. Comput. 35, 269–284 (1980)

    Google Scholar 

  6. Lazarov, R., Mishev, I., Vassilevski, P.: Finite volume methods for convection-diffusion problems. SIAM J. Numer. Anal. 33, 31–55 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Lazarov, R., Pasciak, J., Vassilevski, P.: Coupling mixed and finite volume discretizations of convection-diffusion equations on non-matching grids. In: Proceedings: Finite Volumes for Complex Applications Hermes Science (1999)

    Google Scholar 

  8. Mishev, I.: Finite volume methods on Voronoi meshes. Numer. Methods Partial Differ. Equ. 14, 193–212 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. Riviere, B.: Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation. SIAM, Philadelphia (2008)

    Book  Google Scholar 

  10. Riviere, B., Wheeler, M.: Coupling locally conservative methods for single phase flow. Comput. Geosci. 6, 269–284 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Riviere, B., Yang, X.: Convergence analysis of a coupled method for time-dependent convection-diffusion equations. Numer. Methods Partial Differ. Equ. 30, 133–157 (2013). doi:10.1002/num.21800

    Article  MathSciNet  Google Scholar 

  12. Vassilevski, P., Petrova, S., Lazarov, R.: Finite difference schemes on triangular cell-centered grids with local refinement. SIAM J. Sci. Stat. Comput. 13, 1287–1313 (1992)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

This work was partially funded by NSF-DMS and NHARP.

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Authors and Affiliations

  1. Rice University, 6100 Main Street, Houston, TX, 77005, USA

    Beatrice Riviere & Xin Yang

Authors
  1. Beatrice Riviere
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  2. Xin Yang
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Corresponding author

Correspondence to Beatrice Riviere .

Editor information

Editors and Affiliations

  1. INRIA, Rennes, France

    Jocelyne Erhel

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Géometrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. INRIA, Rennes, France

    Géraldine Pichot

  5. Laboratoire LMNO, Université de Caen, Caen, France

    Taoufik Sassi

  6. New York University Courant Institute, New York, New York, USA

    Olof Widlund

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Riviere, B., Yang, X. (2014). A Domain-Based Multinumeric Method for the Steady-State Convection-Diffusion Equation. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_9

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