A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems
DOI:
https://doi.org/10.4208/aamm.12-m1296Keywords:
Variational discretization, parabolic optimal control problems, finite volume element method, distributed control, Crank-Nicolson.Abstract
In this paper, the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed 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 the theoretical result.