An easily computable error estimator in space and time for the wave equation
For researchers using finite element methods for wave equations, this reduces computational cost of error estimation without sacrificing theoretical guarantees.
The authors propose a cheaper a posteriori error estimator for the wave equation discretized by Newmark and FEM, preserving reliability and optimality while eliminating the need for Laplacian computation at each time step.
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.