Convergence of FEM with interpolated coefficients for semilinear hyperbolic equation

To solve spatially semidiscrete approximative solution of a class of semilinear hyperbolic equations, the finite element method (FEM) with interpolated coefficients is discussed. By use of semidiscrete finite element for linear problem as comparative function, the error estimate in L ∞ -norm is derived by the nonlinear argument in Chen [Structure theory of superconvergence of finite elements, Hunan Press of Science and Technology, Changsha, 2001 (in Chinese)]. This indicates that convergence of FEMs with interpolated coefficients for a semilinear equation is similar to that of classical FEMs.