Adaptive Galerkin Finite Element Methods for the Wave Equation

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 “goaloriented” adaptivity which is based on a posteriori error estimation employing the solutions of auxiliary dual problems. 2000 Mathematics Subject Classification: 35L05, 65M50, 65M60, 74S05.