Wolfgang Bangerth, Michael Geiger, Rolf Rannacher
Adaptive Galerkin finite element methods for the wave equation
Computational Methods in Applied Mathematics, vol. 10 (2010), pp. 3-48.

This paper gives an overview of adaptive discretization methods for linear second-order hyperbolic problems such as the acoustic or the elastic wave equation. The emphasis is on Galerkin-type methods for spatial as well as temporal discretization, which also include variants of the Crank-Nicolson and the Newmark finite difference schemes. The adaptive choice of space and time meshes follows the principle of "goal-oriented" adaptivity which is based on a posteriori error estimation employing the solutions of auxiliary dual problems.

Wolfgang Bangerth
Mon Mar 20 08:38:44 MDT 2017