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Spacetime finite element methods for control problems subject to the wave equation
arXiv - CS - Numerical Analysis Pub Date : 2021-09-16 , DOI: arxiv-2109.07890
Erik Burman, Ali Feizmohammadi, Arnaud Munch, Lauri Oksanen

We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the computational method. The proofs are based on the regularity properties of the control given by the Hilbert Uniqueness Method, together with the stability properties of the numerical scheme. Numerical experiments illustrate the results.

中文翻译:

波动方程控制问题的时空有限元方法

我们考虑波动方程的零可控性问题,并分析在全局非结构化时空网格上制定的稳定有限元方法。我们证明了计算方法给出的近似控制的误差估计。证明基于希尔伯特唯一性方法给出的控制的规律性特性,以及数值方案的稳定性特性。数值实验说明了结果。
更新日期:2021-09-17
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