Abstract
We deal with one subproblem of an air pollution model, the horizontal diffusion, which can be mathematically described by a linear partial differential equation of parabolic type. With different space discretization schemes (like a FDM, FEM), and using the θ-method for time discretization we get a one-step algebraic iteration as a numerical model. The preservation of characteristic qualitative properties of different phenomena is an increasingly important requirement in the construction of reliable numerical models. For that reason we analyze the connection between the shape and time-monotonicity in the continuous and the numerical model, and we give the necessary and sufficient condition to fulfil this property.
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References
Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York (1979)
Faragó, I., Pfeil, T.: Preserving concavity in initial-boundary value problems of parabolic type and its numerical solution. Periodica Mathematica Hungarica 30, 135–139 (1995)
Faragó, I., et al.: A hővezetési egyenlet és numerikus megoldásának kvalitatív tulajdonságai I. Az elsőfokú közelítések nemnegativitása. Alkalmazott Matematikai Lapok 17, 101–121 (1993)
Faragó, I., Horváth, R.: A Review of Reliable Numerical Models for Three-Dimensional Linear Parabolic Problems. Int. J. Numer. Meth. Engng. 70, 25–45 (2007)
Faragó, I., Horváth, R., Korotov, S.: Discrete Maximum Principle for Linear Parabolic Problems Solved on Hybrid Meshes. Appl. Num. Math. 53, 249–264 (2005)
Marchuk, G.I.: Mathematical modeling for the problem of the environment. Studies in Mathematics and Applications, vol. 16. North-Holland, Amsterdam (1985)
Marek, I., Szyld, D.B.: Comparison theorems for weak splittings of bounded operators. Numer. Math. 58, 389–397 (1990)
McRae, G.J., Goodin, W.R., Seinfeld, J.H.: Numerical solution of the atmospheric diffusion equations for chemically reacting flows. Journal of Computational Physics 45, 1–42 (1984)
Mincsovics, M.: Qualitative analysis of the one-step iterative methods and consistent matrix splittings. Special Issue of Computers and Mathematics with Applications (accepted)
Verwer, J.G., Hundsdorfer, W., Blom, J.G.: Numerical Time Integration for Air Pollution Models, Report of CWI, MAS-R9825 (1982)
Zlatev, Z.: Computer Treatment of Large Air Pollution Models. Kluwer Academic Publishers, Dordrecht-Boston-London (1995)
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Georgiev, K., Mincsovics, M. (2008). Qualitatively Correct Discretizations in an Air Pollution Model. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_21
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DOI: https://doi.org/10.1007/978-3-540-78827-0_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78825-6
Online ISBN: 978-3-540-78827-0
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