Aposteriori error analysis for Galerkin finite element methods have proven very successful tool in developing mathematically rigorous adaptive mesh refinement algorithms for implicit/space-time evolution equations. In this work we extend rigorous adaptivity principles to explicit time-stepping for the wave equation.

I will review in the first part of the talk the state of the art for the wave equation. In the second part, I will present recent work in connection to fully practical explicit schemes such as the Leapfrog method and local time step variants thereof.

This talk is mostly based on recent joint work with M Grote, C Santos and earlier work with EH Georgoulis, C Makridakis and J Virtanen.

For further information about the seminar, please visit this webpage.