A two-grid method for finite volume element approximations of second-order nonlinear hyperbolic equations (Q848554)

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 \(V_H\subset\,V_h\). 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.