Jun Pan, Yuelong Tang, Yuchun Hua, Error analysis of a BDF2 scheme combined with finite elements for parabolic optimal control problems, Vol. 2025 (2025), No. 25, pp. 1-12

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DOI: 10.23952/jnfa.2025.25

Received February 14, 2025; Accepted August 31, 2025; Published September 23, 2025

Abstract. This paper proposes a second order convergent discretization scheme in both space and time for parabolic optimal control problems (OCPs). For the state and co-state, the BDF2 scheme and finite elements (FEs) are used for the temporal and spatial discretization, respectively. The control is obtained by variational discretization. The second-order convergence results of all variables in the $L^2$ -norm are rigorously derived. Superconvergence between the projections of the state and co-state and their numerical solutions is established. Two numerical examples are provided to confirm the theoretical analysis results.

How to Cite this Article:
J. Pan, Y. Tang, Y. Hua, Error analysis of a BDF2 scheme combined with finite elements for parabolic optimal control problems, J. Nonlinear Funct. Anal. 2025 (2025) 25.