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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Discretization of continuum physics – a comparison of numerical methods from a physical point of view; pp. 145–154

(Full article in PDF format) doi: 10.3176/proc.2008.3.05


Authors

Heiko Herrmann

Abstract

For numerical calculations in continuum physics partial differential equations and the space-time are discretized. This can be done in different ways. Common approaches are finite difference methods and finite element methods, more rarely finite volume methods are used. Each method has different mathematical properties, which have been discussed in the literature, but they also imply a different physical meaning. This issue is discussed in this article and the connection of finite volume methods to thermodynamics of discrete systems is shown.

Keywords

continuum physics, numerical methods, partial differential equations, finite elements, finite volumes, finite differences.

References

1. Knabner , P. and Angermann , L. Numerik partieller Differentialgleichungen. Springer , 2000.

2. Alberty , J. , Carstensen , C. and Funken , S. A. Remarks around 50 lines of matlab: short finite element implementation. Num. Alg. , 1999 , 20 , 117–137.

3. Muschik , W. , Papenfuβ , C. and Ehrentraut , H. Concepts of Continuum Thermodynamics. Technische Universität Berlin und Kielce University of Technology , 1996.

4. Muschik , W. Aspects of Non-Equilibrium Thermodynamics. World Scientific , Singapore , 1990.

5. Muschik , W. and Berezovski , A. Thermodynamic interaction between two discrete systems in non-equilibrium. J. Non-equilib. Thermodyn. , 2004 , 29 , 237–255.
doi:10.1515/JNETDY.2004.053

6. Muschik , W. and Berezovski , A. Non-equilibrium contact quantities and compound deficiency at interfaces between discrete systems. Proc. Estonian Acad. Sci. Phys. Math. , 2007 , 56 , 133–145.

7. Berezovski , A. and Maugin , G. A. Simulation of thermoelastic wave propagation by means of a composite wave-propagation algorithm. J. Comput. Phys. , 2001 , 168 , 249–264.
doi:10.1006/jcph.2001.6697

8. Bale , D. S. , LeVeque , R. J. , Mitran , S. and Rossmanith , J. A. A wave propagation method for conservation laws and balance laws with spatially varying flux functions. SIAM J. Sci. Comput. , 2003 , 24 , 955–978.
doi:10.1137/S106482750139738X

 
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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December