Strong norm error bounds for quasilinear wave equations under weak CFL-type conditions

In the present paper we consider a class of quasilinear wave equations on a smooth, bounded domain. We discretize it in space with isoparametric finite elements, and apply a semi-implicit Euler and midpoint rule as well as the exponential Euler method to obtain three fully discrete schemes. We derive rigorous error bounds of optimal order for the semi-discretization in space and the fully discrete methods in norms which are stronger than the classical $H^1\times L^2$ energy norm under weak CFL-type conditions.