Answers are grounded in this paper and cite their sources.
Numerical analysis demonstrates rigorous convergence for BDF2 H1-Galerkin schemes in parabolic optimal control problems, highlighting stable approximations without inf-sup constraints.
This paper presents a fully discrete H1-Galerkin mixed finite element approximation for parabolic optimal control problems. For the state and costate variables, the BDF2 scheme and H1-Galerkin mixed finite element method are employed for temporal and spatial discretization, respectively. Since the H1-Galerkin mixed finite element is free from the LBB consistency condition, the unknown scalar and vector functions are therefore approximated by Lagrange elements and Raviart-Thomas mixed elements, respectively. The control is handled via variational discretization. The convergence results of all variables are rigorously derived. Theoretical findings are confirmed by means of some numerical examples.
No takes yet. Share an insight, caveat, or question.
Tang et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: