We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In the absence of external loads, 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 an 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 applications of the method.

Dassi, F., Fumagalli, A., Mazzieri, I., Vacca, G. (2023). Mixed Virtual Element approximation of linear acoustic wave equation. IMA JOURNAL OF NUMERICAL ANALYSIS, 1-28 [10.1093/imanum/drad078].

Mixed Virtual Element approximation of linear acoustic wave equation

Dassi, F;Vacca, G
2023

Abstract

We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In the absence of external loads, 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 an 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 applications of the method.
Articolo in rivista - Articolo scientifico
Mixed Virtual Elements; acoustics wave equations; polygonal meshes; energy conservation
English
13-ott-2023
2023
1
28
reserved
Dassi, F., Fumagalli, A., Mazzieri, I., Vacca, G. (2023). Mixed Virtual Element approximation of linear acoustic wave equation. IMA JOURNAL OF NUMERICAL ANALYSIS, 1-28 [10.1093/imanum/drad078].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/445838
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