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Article

Zlatev, Zahari ; Dimov, Ivan ; Faragó, István ; Georgiev, Krassimir ; Havasi, Ágnes ; Ostromsky, Tzvetan
Application of Richardson extrapolation with the Crank-Nicolson scheme for multi-dimensional advection. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 248-256
MSC: 35L04, 65M06, 65M12 | MR 3204449 | Zbl 1340.65184
Keywords:
multi-dimensional advection equation; Crank-Nicolson scheme; Richardson extrapolation
Summary:
Multi-dimensional advection terms are an important part of many large-scale mathematical models which arise in different fields of science and engineering. After applying some kind of splitting, these terms can be handled separately from the remaining part of the mathematical model under consideration. It is important to treat the multi-dimensional advection in a sufficiently accurate manner. It is shown in this paper that high order of accuracy can be achieved when the well-known Crank-Nicolson numerical scheme is combined with the Richardson extrapolation.
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