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arXiv · 1912.07057

A second order finite element method with mass lumping for wave equations in $H(\mathrm{div})$

Herbert Egger·Bogdan Radu
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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 $H(\mathrm{div})$--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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Herbert Egger, Bogdan Radu. 2019-12-15. A second order finite element method with mass lumping for wave equations in $H(\mathrm{div})$. https://arxiv.org/abs/1912.07057

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