强阻尼wave equation的广义有限元法
A generalized finite element method for the strongly damped wave equation with rapidly varying data
摘要：
本文提出了一种求解强阻尼波动方程的广义有限元法。所提出的方法是基于本地化的正交分解介绍，并被设计为处理独立的阻尼和波的传播速度分别变化。该方法通过自动校正瞬态阶段中的阻尼和稳态阶段中的传播速度来实现。证明了最优阶的收敛性是在$L_2(H^1)$ -范数下进行的，与系数的导数无关.我们提出的数值例子，证实了理论研究结果。
英文摘要：
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent variations in both the damping and the wave propagation speed respectively. The method does so by automatically correcting for the damping in the transient phase and for the propagation speed in the steady state phase. Convergence of optimal order is proven in $L_2(H^1)$-norm, independent of the derivatives of the coefficients. We present numerical examples that confirm the theoretical findings.
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