Adaptive characteristic finite element approximation of convection-diffusion optimal control problems

2012 ◽  
Vol 29 (3) ◽  
pp. 979-998 ◽  
Author(s):  
Hongfei Fu ◽  
Hongxing Rui
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problems ◽  
Finite Element Approximation ◽  
Control Problems ◽  
Element Approximation ◽  
Convection Diffusion ◽  
Characteristic Finite Element

Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients

2013 ◽  
Vol 3 (3) ◽  
pp. 209-227
Author(s):  
Yuelong Tang ◽  
Yanping Chen
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problems ◽  
Finite Element Approximation ◽  
Euler Method ◽  
Time Dependent ◽  
Control Problems ◽  
Element Approximation ◽  
Time Discretisation ◽  
Backward Euler

AbstractIn this article, a fully discrete finite element approximation is investigated for constrained parabolic optimal control problems with time-dependent coefficients. The spatial discretisation invokes finite elements, and the time discretisation a nonstandard backward Euler method. On introducing some appropriate intermediate variables and noting properties of the L2 projection and the elliptic projection, we derive the superconvergence for the control, the state and the adjoint state. Finally, we discuss some numerical experiments that illustrate our theoretical results.

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