A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems (Advances in Applied Mathematics and Mechanics, 2013)
In this paper, the Crank-Nicolson linear finite volume elementmethod is applied to solve the distributed optimal control problemsgoverned by a parabolic equation. The optimal convergent order $\mathcal{O}(h^2+k^2)$ is obtained for the numerical solution in a discrete $L^2$-norm. A numerical experiment is presented to test thetheoretical result.