Spacetime finite element methods for control problems subject to the wave equation

被引：4

作者：

Burman, Erik ^{[1
]}

Feizmohammadi, Ali ^{[2
]}

Munch, Arnaud ^{[3
]}

Oksanen, Lauri ^{[4
]}

机构：

[1] UCL, Dept Math, Gower St, London WC1E 6BT, England

[2] Univ Toronto, Dept Math, 3359 Mississauga Rd Deerfield Hall, Mississauga, ON L5L 1C6, Canada

[3] Univ Clermont Auvergne, Lab Math Blaise Pascal, CNRS, LMBP, F-63000 Clermont Ferrand, France

[4] Univ Helsinki, Dept Math & Stat, PO 68, Helsinki 00014, Finland

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2023年 / 29卷

基金：

英国工程与自然科学研究理事会;

关键词：

Wave equation; control; finite element method; space time; stabilisation; BOUNDARY CONTROLLABILITY; NUMERICAL-METHOD; APPROXIMATION; STABILIZATION; INTERPOLATION;

D O I：

10.1051/cocv/2023028

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页数：40

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