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Zbl 1221.65235
Zhang, Tong; Zhong, He; Zhao, Jing
A full discrete two-grid finite-volume method for a nonlinear parabolic problem. (English)
[J] Int. J. Comput. Math. 88, No. 8, 1644-1663 (2011). ISSN 0020-7160; ISSN 1029-0265/e

A nonlinear convection-diffusion problem in $\mathbb{R}^2$ is solved numerically with a fully discrete two-grid finite volume method. The method is based on solving the problem on a coarse mesh space and then take the resulting solution as the starting point to solve a linearized parabolic equation on the fine grid. The treatment largely parallels the one carried out by the first author [Appl. Math. Comput. 217, No.~19, 7546--7556 (2011; Zbl 1221.65234)] with a semi-discrete finite volume method. The numerical example chosen to illustrate the analysis is also the same.
[Fernando Casas (Castellon)]

MSC 2000:: *65M08
35K55 Nonlinear parabolic equations
65M15 Error bounds (IVP of PDE)
65M55 Multigrid methods; domain decomposition (IVP of PDE)

Keywords: finite volume method; convection-diffusion problem; error estimate; two-grid method; nonlinear parabolic problem; nonlinear convection-diffusion problem; numerical example

Citations: Zbl 1221.65234

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