Abstract
We consider the efficient numerical approximation of acoustic wave propagation in time domain by a finite element method with mass lumping. In the presence of internal damping, the problem can be reduced to a second order formulation in time for the velocity field alone. For the spatial approximation we consider H(div)-conforming finite elements of second order. In order to allow for an efficient time integration, we propose a mass-lumping strategy based on approximation of the L 2-scalar product by inexact numerical integration which leads to a block-diagonal mass matrix. A careful error analysis allows to show that second order accuracy is not reduced by the quadrature errors which is illustrated also by numerical tests.
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Acknowledgements
This work was supported by the German Research Foundation (DFG) via grants TRR 146 C3, TRR 154 C4, Eg-331/1-1, and through the “Center for CE” at TU Darmstadt.
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Egger, H., Radu, B. (2021). A Second Order Finite Element Method with Mass Lumping for Wave Equations in H(div). In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_78
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DOI: https://doi.org/10.1007/978-3-030-55874-1_78
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