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arXiv · 1805.05789

Extended finite element methods for optimal control problems governed by Poisson equation in non-convex domains

Tao Wang·Chao Chao Yang·Xiaoping Xie
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Abstract

This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous problems, and apply an XFEM with a cut-off function and a classic XFEM with a fixed enrichment area to discretize the state and co-state equations. Optimal error estimates are derived for the state, co-state and control. Numerical results confirm our theoretical results.

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Tao Wang, Chao Chao Yang, Xiaoping Xie. 2018-05-13. Extended finite element methods for optimal control problems governed by Poisson equation in non-convex domains. https://arxiv.org/abs/1805.05789

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