TY - JOUR
T1 - Numerical Methods for Constrained Elliptic Optimal Control Problems with Rapidly Oscillating Coefficients
AU - Chen , Yanping
AU - Tang , Yuelong
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 235
EP - 247
PY - 2018
DA - 2018/02
SN - 1
DO - http://doi.org/10.4208/eajam.071010.250411a
UR - https://global-sci.org/intro/article_detail/eajam/10906.html
KW - Optimal control problems, finite element method, multiscale finite element method, homogenization, convergence analysis.
AB - <p style="text-align: justify;">In 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 $\varepsilon$ is small enough, while multiscale
finite element method is useful for any parameter <span style="text-align: justify;">$\varepsilon$</span>.</p>