A second order finite element method with mass lumping for wave equations in $H(\mathrm{div})$
Numerical Analysis
2019-12-17 v1 Numerical Analysis
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 --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 -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.
Cite
@article{arxiv.1912.07057,
title = {A second order finite element method with mass lumping for wave equations in $H(\mathrm{div})$},
author = {Herbert Egger and Bogdan Radu},
journal= {arXiv preprint arXiv:1912.07057},
year = {2019}
}