Heterogeneous Multiscale Method for Optimal Control Problem Governed by Elliptic Equations with Highly Oscillatory Coefficients

2018 ◽  
Vol 36 (5) ◽  
pp. 644-660 ◽  
Author(s):  
Liang Ge
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elliptic Equations ◽  
Multiscale Method ◽  
Highly Oscillatory ◽  
Heterogeneous Multiscale

scholarly journals Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
JongKyum Kwon ◽  
Soorok Ryu ◽  
Philsu Kim ◽  
Sang Dong Kim
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elliptic System ◽  
Elliptic Equations ◽  
Spectral Element ◽  
Uniform Bounds ◽  
Element System ◽  
Element Discretizations

The uniform bounds on eigenvalues ofB^h2−1A^N2are shown both analytically and numerically by theP1finite element preconditionerB^h2−1for the Legendre spectral element systemA^N2u¯=f¯which is arisen from a coupled elliptic system occurred by an optimal control problem. The finite element preconditioner is corresponding to a leading part of the coupled elliptic system.

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