AbstractIn this paper, we discuss a priori error estimates for the finite volume element approximation of optimal control problem governed by Stokes equations. Under some reasonable assumptions, we obtain optimal $L^{2}$
L
2
-norm error estimates. The approximate orders for the state, costate, and control variables are $O(h^{2})$
O
(
h
2
)
in the sense of $L^{2}$
L
2
-norm. Furthermore, we derive $H^{1}$
H
1
-norm error estimates for the state and costate variables. Finally, we give some conclusions and future works.
Error estimates in $ L^2 $ and $ L^\infty $ norms of finite volume method for the bilinear elliptic optimal control problem