论文标题
具有快速变化的数据的强阻尼波方程的广义有限元方法
A generalized finite element method for the strongly damped wave equation with rapidly varying data
论文作者
论文摘要
我们提出了一种具有高度变化系数的强阻尼波方程的广义有限元方法。该方法基于引入的局部正交分解，旨在分别处理阻尼和波传播速度的独立变化。该方法是通过在瞬态相中自动校正阻尼和在稳态相中的传播速度来做到的。最佳顺序的收敛性在$ L_2（H^1）$ - 标准中证明，与系数的衍生物无关。我们提出了确认理论发现的数值示例。
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.
