scholarly journals A multiscale finite element method for optimal control problems governed by the elliptic homogenization equations

2010 ◽  
Vol 60 (3) ◽  
pp. 390-398 ◽  
Author(s):  
Jian Li
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Element Method

Numerical Methods for Constrained Elliptic Optimal Control Problems with Rapidly Oscillating Coefficients

2011 ◽  
Vol 1 (3) ◽  
pp. 235-247 ◽  
Author(s):  
Yanping Chen ◽  
Yuelong Tang
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Numerical Methods ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Multiscale Finite Element Method ◽  
Oscillating Coefficients ◽  
Multiscale Finite Element ◽  
Element Method

AbstractIn this paper we use two numerical methods to solve constrained optimal control problems governed by elliptic equations with rapidly oscillating coefficients: one is finite element method and the other is multiscale finite element method. We derive the convergence analysis for those two methods. Analytical results show that finite element method can not work when the parameter ε is small enough, while multiscale finite element method is useful for any parameter ε.

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