Mixed Virtual Element approximation of linear acoustic wave equation
Numerical Analysis
2022-09-26 v1 Numerical Analysis
Abstract
We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time the semi-discrete problem we consider a classical theta-method scheme. We carry out the stability and convergence analysis in the energy norm for the semi-discrete problem showing optimal rate of convergence with respect to the mesh size. We further study the property of energy conservation for the fully-discrete system. Finally, we present some verification tests as well as engineering application of the method.
Cite
@article{arxiv.2209.11603,
title = {Mixed Virtual Element approximation of linear acoustic wave equation},
author = {Franco Dassi and Alessio Fumagalli and Ilario Mazzieri and Giuseppe Vacca},
journal= {arXiv preprint arXiv:2209.11603},
year = {2022}
}