Abstract
Two conservative schemes for the nonstationary advection-diffusion equation featuring nonlinear monotone finite volume methods (FVMON) are considered. The first one is an operator-splitting scheme which uses discontinuous finite elements for the advection operator discretization and FVMON for the diffusion operator. The second one introduces another type of FVMON and is implicit second-order BDF in time. A brief description of the schemes and their properties is given. A numerical study is conducted in order to check their convergence and to compare them with conventional methods.
MSC2010:65M08
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Acknowledgements
This work has been supported in part by RFBR grants 09-01-00115-a, 11-01-00971-a and the federal program “Scientific and scientific-pedagogical personnel of innovative Russia”
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Vassilevski, Y., Danilov, A., Kapyrin, I., Nikitin, K. (2011). Application of Nonlinear Monotone Finite Volume Schemes to Advection-Diffusion Problems. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_80
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DOI: https://doi.org/10.1007/978-3-642-20671-9_80
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