Implementation of Bilinear Nonconforming Finite Elements in an Eulerian Air Pollution Model: Results Obtained by Using the Rotational Test

  • Anton Antonov
  • Krassimir Georgiev
  • Emilia Komsalova
  • Zahari Zlatev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2542)


The implementation of bilinear nonconforming finite elements in the advection-diffusion part of an Eulerian air pollution model for long-range transport of air pollutants is discussed. The final aim will be to implement such elements in the operational version of a particular air pollution model, the Danish Eulerian Model (DEM). One-dimensional first-order finite element method is currently used during the space discretization of the advection-diffusion part in the operational version of DEM. The application of more accurate methods in the advection part of DEM is desirable. Two different bilinear nonconforming finite elements have been implemented and compared. The rotational test is very popular among researchers in the fields of meteorology and environmental modelling. Numerical results that are obtained in the treatment of the rotational test with the new finite element schemes show that these elements have good qualities and, therefore, it is worthwhile to replace the one-dimensional first-order finite elements with one of the bilinear nonconforming finite elements considered in the paper.

Key words

air pollution modelling rotational test nonconforming finite elements 


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  1. 1.
    Antonov, A.: Object-oriented framework for large scale air pollution models. PhD Thesis, The Technical University of Denmark, Copenhagen, Denmark (2001)Google Scholar
  2. 2.
    Brandt, J. et al: Operational air pollution forecasts from European to local scale. Atmospheric Environment, 35, Suppl. No. 1 (2001) S91–S98.CrossRefGoogle Scholar
  3. 3.
    Crowley, W. P.: Numerical advection experiments. Monthly Weather Review, 96 (1968) 1–11.CrossRefGoogle Scholar
  4. 4.
    Georgiev, K., Zlatev, Z.: Application of parallel algorithms in an air pollution model. In: Z. Zlatev et al (eds.): Large Scale Computations in Air pollution Modelling. NATO Science, Series 2. Environmental Security, 57, Kluwer Acad. Publ. (1999) 173–184.Google Scholar
  5. 5.
    Georgiev, K., Zlatev, Z.: Parallel sparse matrix algorithms for air pollution models. Parallel and Distributed Computing Practices, Vol. 2, 4 (1999) 429–442.Google Scholar
  6. 6.
    Georgiev, K., Zlatev, Z.: Running large-scale air pollution models on parallel computers. In: Air Pollution Modelling and its application XIII, Kluwer Academic/Plenum Press, London-New York (2000) 223–232.Google Scholar
  7. 7.
    John, V, Maubach, J., Tobiska, L.: Nonconforming streamline-diffusion finite element methods for convection-diffusion problems. Numer. Math. 78 (1997) 165–188.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    McRae, G. J., Goodin, W. R., and Seinfeld, J. H.: Numerical solution of the atmospheric diffusion equations for chemically reacting flows. Journal of Computational Physics, 45 (1984) 1–42.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Marchuk, G. I.: Mathematical modeling for the problem of the environment. North-Holland, Amsterdam (1985)Google Scholar
  10. 10.
    Molenkampf, C. R.: Accuracy of finite-difference methods applied to the advection equation. Journal of Applied Meteorology, 7 (1968) 160–167.CrossRefGoogle Scholar
  11. 11.
    Petrova, S., Tobiska, L., Vassilevski, P.: Multigrid methods based on matrixdependent coarse spaces for nonconforming streamline-diffusion finite element discretization of convection-diffusion problems. East-West J. Numer. Math. 8 (2000) 223–242.zbMATHMathSciNetGoogle Scholar
  12. 12.
    Rannacher, R., Turek, S.: Simple nonconforming quadrilateral Stokes element. Numer. Meth. for PDE’s, 8 (1992) 97–111.zbMATHMathSciNetGoogle Scholar
  13. 13.
    Wolfram, S.: Mathematica: a system for doing mathematics by computer. Wolfram Media, Cambridge Univ. Press, Fourth Edition (1999)Google Scholar
  14. 16.
    Zlatev, Z.: Computer treatment of large air pollution models. Kluwer Academic Publishers, Dordrecht-Boston-London (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Anton Antonov
    • 1
  • Krassimir Georgiev
    • 2
  • Emilia Komsalova
    • 2
  • Zahari Zlatev
    • 3
  1. 1.Wolfram Research Inc.ChampaignUSA
  2. 2.Central Laboratory for Parallel ProcessingSofiaBulgaria
  3. 3.National Environmental Research InstituteRoskildeDenmark

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