Computation of minimal norm control asymptotics relative to the null controllability of non-standard parabolic-like dynamics

Abstract Semidiscrete finite element method (FEM) approximation schemes are presented for the null controllability of two non-standard parabolic PDE control systems. The key feature here is that the null controllers being approximated exhibit the asymptotics of the associated minimal energy function. The main driver is the appropriate use of a result in [R. Triggiani, Optimal estimates of norms of fast controls in exact null controllability of two non-classical abstract parabolic systems, Advances in Differential Equations 8 (2) (2003) 189–229.], which was originally devised to derive the sharp minimal norm control asymptotics for the fully continuous problem.