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Wolfgang Bangerth and
Rolf Rannacher

** Adaptive finite element techniques for the
acoustic wave equation**

Journal of Computational Acoustics, vol. 9, no. 2
(2001), pp. 575-591.

We present an adaptive finite element method for solving the acoustic
wave equation. Using a global duality argument and Galerkin orthogonality,
we derive an identity for the error with respect to an arbitrary functional
output of the solution. The error identity is evaluated by solving the
dual problem numerically. The resulting local cell-wise error indicators
are used in adaptation process. In this way, the space-time mesh can be
tailored for the efficient computation of the quantity of interest.
We give an overview of the implementation of the proposed method and
illustrate its performance by several numerical examples.

*Wolfgang Bangerth*

* Thu Feb 15 22:24:40 MST 2018 *