NASep 21, 2017
Time and space adaptivity of the wave equation discretized in time by a second order schemeOlga Gorynina, Alexei Lozinski, Marco Picasso
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.
NAOct 22, 2017
An easily computable error estimator in space and time for the wave equationOlga Gorynina, Alexei Lozinski, Marco Picasso
We propose a cheaper version of \textit{a posteriori} error estimator from arXiv:1707.00057 for the linear second-order wave equation discretized by the Newmark scheme in time and by the finite element method in space. The new estimator preserves all the properties of the previous one (reliability, optimality on smooth solutions and quasi-uniform meshes) but no longer requires an extra computation of the Laplacian of the discrete solution on each time step.