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Wolfgang Bangerth and
Rolf Rannacher

**Finite element approximation of
the acoustic wave equation: Error estimation and mesh
adaptation**

East-West Journal of Numerical Mathematics, vol. 7,
no. 4 (1999), pp. 263-282.

We present an approach to solving the acoustic wave equation by adaptive
finite element methods. Using a global duality argument and Galerkin
orthogonality, we obtain a residual-based error representation with respect to an
arbitrary functional of the solution. This results in numerically
evaluatable error estimates which are used for mesh refinement. In this way,
very economical and highly localized space-time
meshes can be generated which are tailored to the efficient computation of
the quantity of interest. We demonstrate the performance and some of the
mechanisms acting in our approach by numerical examples.

*Wolfgang Bangerth*

* Thu May 4 14:55:17 MDT 2017 *