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A two-grid method for finite volume element approximations of second-order nonlinear hyperbolic equations. (English) Zbl 1190.65150

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 Ω, 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 V h .

An H 1 error estimate of order h+H 3 log|H| is proved. A numerical test is presented to justify the efficiency of the method.

MSC:
65M55Multigrid methods; domain decomposition (IVP of PDE)
65M08Finite volume methods (IVP of PDE)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M20Method of lines (IVP of PDE)
35L70Nonlinear second-order hyperbolic equations
65M15Error bounds (IVP of PDE)