Full Text: PDF
DOI: 10.23952/jnfa.2024.1
Received March 23, 2023; Accepted December 4, 2023; Published January 12, 2024
Abstract. In this paper, we propose the Crank-Nicolson splitting positive definite mixed finite element approximation of parabolic control problems with control constraints. For the state and co-state variables, the Crank-Nicolson scheme is used for time discretization and the first-order Raviart-Thomas mixed element is applied for space discretization. The numerical solution of the control variable is obtain by variational discretization. Based on some regularity assumptions, we derive optimal priori error estimates of the control, state and co-state. Some numerical examples confirm the theoretical investigations.
How to Cite this Article:
Y. Tang, Y. Hua, Crank-Nicolson splitting positive definite mixed element discretization of parabolic control problems, J. Nonlinear Funct. Anal. 2024 (2024) 1.