Error estimates of finite volume method for Stokes optimal control problem

• الحاوية / القاعدة: Journal of Inequalities and Applications
• المؤلفون الرئيسيون: Lin Lan, Ri-hui Chen, Xiao-dong Wang, Chen-xia Ma, Hao-nan Fu
• التنسيق: مقال
• اللغة: الإنجليزية
• منشور في: SpringerOpen 2021-01-01
• الموضوعات: Optimal control problem; Stokes equations; Finite volume method; A priori error estimates; Variational discretization
• الوصول للمادة أونلاين: https://doi.org/10.1186/s13660-020-02532-4
• تدمد: 1029-242X

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.