Error estimates of finite volume method for Stokes optimal control problem

• Main Authors: Lin Lan, Ri-hui Chen, Xiao-dong Wang, Chen-xia Ma, Hao-nan Fu
• Format: Article
• Language: English
• Published: SpringerOpen 2021-01-01
• Series: Journal of Inequalities and Applications
• Subjects: Optimal control problem; Stokes equations; Finite volume method; A priori error estimates; Variational discretization
• Online Access: https://doi.org/10.1186/s13660-020-02532-4

Abstract In this paper, we discuss a priori error estimates for the finite volume element approximation of optimal control problem governed by Stokes equations. Under some reasonable assumptions, we obtain optimal L 2 $L^{2}$ -norm error estimates. The approximate orders for the state, costate, and control variables are O ( h 2 ) $O(h^{2})$ in the sense of L 2 $L^{2}$ -norm. Furthermore, we derive H 1 $H^{1}$ -norm error estimates for the state and costate variables. Finally, we give some conclusions and future works.