A new MOX report entitled “Mixed Virtual Element approximation of linear acoustic wave equation” by Dassi, F.; Fumagalli, A.; Mazzieri, I.; Vacca, G. has appeared in the MOX Report Collection.
The report can be donwloaded at the following link:
https://www.mate.polimi.it/biblioteca/add/qmox/65/2022.pdf
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.
