A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions

In this work we present a unified error analysis for abstract space discretizations of nonlinear wave-type equations. This yields an error bound in terms of discretization and interpolation errors that can be applied to various equations and space discretizations fitting in the abstract setting. We use the unified error analysis to prove novel convergence rates for a non-conforming finite element space discretization of wave equations with nonlinear acoustic boundary conditions and illustrate the error bound by some numerical experiments.