The Convergence and Superconvergence of a MFEM For Elliptic Optimal Control Problems
Mathematics and Natural Sciences
In this paper, we investigate a mixed finite element method (MFEM) for the elliptic optimal control problems (OCPs) with a distributive control. The state variable and adjoint state variable are approximated by the conforming rectangular Q11 + Q01 × Q10 elements pair. The discrete B-B condition is satisfied automatically, which is usually considered to be the key point of the MFEM. The control is then obtained by the orthogonal projection through the adjoint state. Optimal orders of convergence are derived for the above mentioned variables. Furthermore, superclose and superconvergence results are also established under certain reasonable regularity assumptions. Some numerical results are provided to verity the theoretical analysis. At last, the proposed method is extended to some other low order conforming and nonconforming elements.
Advances in Applied Mathematics and Mechanics
(2020). The Convergence and Superconvergence of a MFEM For Elliptic Optimal Control Problems. Advances in Applied Mathematics and Mechanics, 12(2), 527-544.
Available at: https://aquila.usm.edu/fac_pubs/17916