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arXiv · 2209.11603

Mixed Virtual Element approximation of linear acoustic wave equation

Franco Dassi·Alessio Fumagalli·Ilario Mazzieri·Giuseppe Vacca
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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.

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Franco Dassi, Alessio Fumagalli, Ilario Mazzieri, Giuseppe Vacca. 2022-09-23. Mixed Virtual Element approximation of linear acoustic wave equation. https://arxiv.org/abs/2209.11603

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