Time and space adaptivity of the wave equation discretized in time by a second order scheme
Provides rigorous error control for adaptive algorithms solving wave equations, benefiting computational scientists and engineers.
The paper derives optimal-order a posteriori error bounds for the linear wave equation discretized with the Newmark scheme in time and finite elements in space, confirmed by numerical experiments showing estimator-error equivalence.
The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. Error estimates are derived in the $L^{\infty}$-in-time/energy-in-space norm. Numerical experiments are reported for several test cases and confirm equivalence of the proposed estimators and the true error.