Mixed Virtual Element approximation of linear acoustic wave equation

被引：2

作者：

Dassi, Franco ^{[1
]}

Fumagalli, Alessio ^{[2
]}

Mazzieri, Ilario ^{[2
]}

Vacca, Giuseppe ^{[3
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicazioni, Via R Cozzi 55, I-20125 Milan, Italy

[2] Politecn Milan, MOX Dipartimento Matemat, Pza L da Vinci 32, I-20133 Milan, Italy

[3] Univ Bari, Dipartimento Matemat, Via E Orabona 4, I-70125 Bari, Italy

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2024年 / 44卷 / 05期

关键词：

Mixed Virtual Elements; acoustics wave equations; polygonal meshes; energy conservation; DISCONTINUOUS GALERKIN METHOD; 2ND-ORDER ELLIPTIC PROBLEMS; HYBRID HIGH-ORDER; FINITE-ELEMENTS; PROPAGATION; CONVERGENCE; STABILITY;

D O I：

10.1093/imanum/drad078

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2864 / 2891

页数：28

共 71 条

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Adams R.A., 2003, Pure and Applied Mathematics, V140

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