A Fully Discrete Numerical Control Method for the Wave Equation
A Fully Discrete Numerical Control Method for the Wave Equation
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DOI：
10.1137/19m1249424
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发表时间：
2019-03
期刊：
影响因子：
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通讯作者：
E. Burman;A. Feizmohammadi;L. Oksanen
中科院分区：
文献类型：
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作者：
E. Burman;A. Feizmohammadi;L. Oksanen
对波动方程的内零能控性问题提出了一种全离散有限元方法。对于数值格式，考虑了空间上的分段仿射连续元和时间上的有限差分。我们表明，如果尖锐的几何控制条件成立，我们的数值方案产生的最佳收敛速度相对于时空网格参数h$。该方法是基于离散格式的稳定项的设计，其目标是使计算误差最小化。
We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piece-wise affine continuous elements in space and finite differences in time are considered. We show that if the sharp geometric control condition holds, our numerical scheme yields the optimal rate of convergence with respect to the space-time mesh parameter $h$. The approach is based on the design of stabilization terms for the discrete scheme with the goal of minimizing the computational error.