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Zbl 1190.65150
Chen, Chuanjun; Liu, Wei
A two-grid method for finite volume element approximations of second-order nonlinear hyperbolic equations. (English)
[J] J. Comput. Appl. Math. 233, No. 11, 2975-2984 (2010). ISSN 0377-0427

The authors consider a second order nonlinear hyperbolic equation. A semidiscrete finite volume element method, based on the two-grid method, is suggested and analyzed. The idea of the two grid method is to reduce the nonlinear and nonsymmetric problem on a fine grid into a linear and symmetric problem on a coarse grid. The basic mechanisms are two quasi uniform triangulations of $\Omega$, $T_H$ and $T_h$, with two different sizes $H$ and $h$ ($H>h$), and the corresponding finite element spaces $V_H$ and $V_h$ which satisfy $V_H\subset\,V_h$. \par An $H^1$ error estimate of order $h+H^3\log\vert\,H\vert$ is proved. A numerical test is presented to justify the efficiency of the method.
[Abdallah Bradji (Tebessa)]

MSC 2000:: *65M55 Multigrid methods; domain decomposition (IVP of PDE)
65M08
65M60 Finite numerical methods (IVP of PDE)
65M20 Method of lines (IVP of PDE)
35L70 Second order nonlinear hyperbolic equations
65M15 Error bounds (IVP of PDE)

Keywords: two grid method; second order non linear hyperbolic equation; finite volume element method; error estimates; numerical examples; semidiscretization

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