Error Analysis of Fully Discrete Finite Element Approximations to an Optimal Control Problem Governed by a Time-Fractional PDE

2019 ◽  
Vol 57 (1) ◽  
pp. 241-263
Author(s):  
Max Gunzburger ◽  
Jilu Wang
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Error Analysis ◽  
Control Problem ◽  
Fully Discrete ◽  
Finite Element Approximations ◽  
Fractional Pde ◽  
Discrete Finite Element

Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints

2013 ◽  
Vol 3 (2) ◽  
pp. 138-153 ◽  
Author(s):  
Y. Tang ◽  
Y. Hua
Keyword(s):  
Optimal Control ◽  
Finite Elements ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Euler Method ◽  
Integral Constraints ◽  
Fully Discrete ◽  
Time Discretisation ◽  
Backward Euler ◽  
Discrete Finite Element

AbstractA quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical examples are performed to confirm theoretical results.

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