论文标题
线性声波方程的混合虚拟元素近似
Mixed Virtual Element approximation of linear acoustic wave equation
论文作者
论文摘要
我们为声波方程的一阶形式设计了一种混合的虚拟元素方法。在没有外部载荷的情况下，半分化方法恰好可以保存系统能量。为了及时整合半混凝土问题，我们考虑了经典的theta方法方案。对于半滴定问题，我们在能量规范中进行了稳定性和收敛分析，显示了相对于网格尺寸的最佳收敛速率。我们进一步研究了全污染系统能源保护的特性。最后，我们提供了一些验证测试以及该方法的工程应用。
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.
