Abstract
In this paper, adaptive virtual element method (VEM) approximation of optimal control problem governed by Stokes equations with control constraints is discussed. The virtual element discrete scheme of the optimal control problem is constructed by polynomial projections and variational discretization of the control variable. Based on the a posteriori error estimates of VEM for Stokes equations and approximated error equivalence between the solutions of the optimal control problem and the solutions of the state and adjoint equations, we build up upper and lower bounds for the a posteriori error estimates of the optimal control problem. It proves that the a posteriori error indicator is reliable and efficient. The theoretical findings are illustrated by the numerical experiments.
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The research was supported by National Natural Science Foundation of China (No. 11971276, 12171287).
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Li, Y., Wang, Q. & Zhou, Z. Adaptive Virtual Element Method for Optimal Control Problem Governed by Stokes Equations. J Sci Comput 97, 63 (2023). https://doi.org/10.1007/s10915-023-02377-1
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DOI: https://doi.org/10.1007/s10915-023-02377-1
Keywords
- Virtual element method
- Optimal control problem
- Stokes equations
- A posteriori error analysis
- Adaptive VEM algorithm