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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*

* Wed Apr 19 13:44:46 MDT 2017 *