Some error estimates of finite volume element method for parabolic optimal control problems

2012 ◽  
Vol 35 (2) ◽  
pp. 145-165 ◽  
Author(s):  
Xianbing Luo ◽  
Yanping Chen ◽  
Yunqing Huang ◽  
Tianliang Hou
Keyword(s):  
Optimal Control ◽  
Error Estimates ◽  
Finite Volume ◽  
Optimal Control Problems ◽  
Volume Element ◽  
Control Problems ◽  
Finite Volume Element Method ◽  
Finite Volume Element ◽  
Parabolic Optimal Control ◽  
Element Method

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.

HIGH-ORDER UPWIND FINITE VOLUME ELEMENT METHOD FOR FIRST-ORDER HYPERBOLIC OPTIMAL CONTROL PROBLEMS

2016 ◽  
Vol 57 (4) ◽  
pp. 482-498
Author(s):  
QIAN ZHANG ◽  
JINLIANG YAN ◽  
ZHIYUE ZHANG
Keyword(s):  
Optimal Control ◽  
Error Estimates ◽  
Finite Volume ◽  
Optimal Control Problems ◽  
Volume Element ◽  
High Order ◽  
Control Problems ◽  
Finite Volume Element Method ◽  
First Order ◽  
Finite Volume Element

We present a high-order upwind finite volume element method to solve optimal control problems governed by first-order hyperbolic equations. The method is efficient and easy for implementation. Both the semi-discrete error estimates and the fully discrete error estimates are derived. Optimal order error estimates in the sense of $L^{2}$-norm are obtained. Numerical examples are provided to confirm the effectiveness of the method and the theoretical results.

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