数学
有限差分
有限差分法
过滤(数学)
波动方程
数学分析
边界(拓扑)
边值问题
应用数学
纯数学
作者
Pierre Lissy,Ionel Roventa
摘要
We consider a finite-differences semi-discrete scheme for the approximation of boundary controls for the one-dimensional wave equation. The high frequency numerical spurious oscillations lead to a loss of the uniform (with respect to the mesh-size) controllability property of the semi-discrete model in the natural setting. We prove that, by filtering the high frequencies of the initial data in an optimal range, we restore the uniform controllability property. Moreover, we obtain a relation between the range of filtration and the minimal time of control needed to ensure the uniform controllability.
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