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 Jun 14 16:00:01 MDT 2018