Error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations

AbstractOptimal order rates of convergence are proved for fully discrete approximations for nonlinear second order hyperbolic equations which are based on a finite element approximation in the space variables and a single step method in the time variable. The r.h.s. of the differential equation can depend on u, u1or ∇u and the coefficients can depend on u. This paper generalizes the work of Bales where the r.h.s. and coefficients were allowed to depend on u