ERROR ESTIMATES OF SEMIDISCRETE FINITE ELEMENT APPROXIMATION FOR MINIMAL TIME IMPULSE CONTROL PROBLEMS

. This paper is concerned with finite element approximation for the minimal time optimal control problem (TP) of the heat equation with impulse controls at some control instants. To this end, with the aid of Pontryagin's Maximum Principle, we first get the H1-regularity estimate of the optimal control by making use of the semigroup method and the unique continuation property. Then, following the high order regularity estimate of the optimal control, the error estimate of the optimal time between the original impulse control problem (TP) and the semidiscrete impulse control problem (TPhl) is established.