Hongbo Chen, A new two-grid $P_0^2$-$P_1$ mixed finite element algorithm for general elliptic optimal control problems, Vol. 2022 (2022), Article ID 41, pp. 1-11

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DOI: 10.23952/jnfa.2022.41

Received July 7, 2022; Accepted September 10, 2022; Published November 8, 2022

Abstract In this paper, a new two-grid mixed finite element scheme for distributed optimal control governed by general elliptic equations is presented. $P_0^2$ – $P_1$ mixed finite elements and piecewise constant functions are used for spatial discretization. Convergence of the proposed two-grid algorithm is discussed. In the two-grid scheme, the solution of the elliptic optimal control problem on a fine grid is reduced to the solution of the elliptic optimal control problem on a much coarser grid and the solution of a symmetric linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy.

How to Cite this Article:
H. Chen, A new two-grid $P_0^2$ – $P_1$ mixed finite element algorithm for general elliptic optimal control problems, J. Nonlinear Funct. Anal. 2022 (2022) 41.