Abstract: A posteriori error analysis for Galerkin finite element methods have proven very successful tool in developing mathematically rigorous adaptive mesh refinement algorithms for elliptic and parabolic equations. Progress for the wave equation has picked up in recent years. I will review in the first part of the talk the state of the art. In the second part, I will present recent work of mine and the first two coauthors below,in connection to fully practical explicit schemes such as the Leapfrog method and local time step variants thereof.
This is based on joint works with M Grote, C Santos, EH Georgoulis, C Makridakis and J Virtanen.