TY - JOUR
T1 - Some Error Estimates of Finite Volume Element Approximation for Elliptic Optimal Control Problems
AU - X. Luo, Y. Chen & Y. Huang
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 697
EP - 711
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/590.html
KW - finite volume element method, variational discretization, optimal control problems, elliptic equation, distributed control.
AB - <p style="text-align: justify;">In this paper, finite volume element method is applied to solve the distributed optimal
control problems governed by an elliptic equation. We use the method of variational discretization
concept to approximate the problems. The optimal order error estimates in $L^2$ and $L^∞$-norm are
derived for the state, costate and control variables. The optimal $H^1$ and $W^{1,∞}$-norm error estimates
for the state and costate variables are also obtained. Numerical experiments are presented
to test the theoretical results.</p>