scholarly journals A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for a Hyperbolic Optimal Control Problem

2016 ◽  
Vol 32 (5) ◽  
pp. 1331-1356
Author(s):  
Xianbing Luo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Error Estimates ◽  
Finite Volume ◽  
A Priori ◽  
Volume Element ◽  
Finite Volume Element Method ◽  
Finite Volume Element ◽  
Priori Error Estimates

scholarly journals Error estimates of finite volume method for Stokes optimal control problem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lin Lan ◽  
Ri-hui Chen ◽  
Xiao-dong Wang ◽  
Chen-xia Ma ◽  
Hao-nan Fu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Error Estimates ◽  
Finite Volume ◽  
Stokes Equations ◽  
A Priori ◽  
The State ◽  
Element Approximation ◽  
Norm Error

AbstractIn 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.

A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems

2013 ◽  
Vol 5 (05) ◽  
pp. 688-704 ◽  
Author(s):  
Xianbing Luo ◽  
Yanping Chen ◽  
Yunqing Huang
Keyword(s):  
Optimal Control ◽  
Finite Volume ◽  
Optimal Control Problems ◽  
A Priori ◽  
Volume Element ◽  
Control Problems ◽  
Finite Volume Element Method ◽  
Finite Volume Element ◽  
Element Method ◽  
Crank Nicolson

AbstractIn this paper, the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation. The optimal convergent orderO(h2+k2) is obtained for the numerical solution in a discreteL2-norm. A numerical experiment is presented to test the theoretical result.

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