B-Spline Finite Element Method for Optimal Control Problems with a Thin Film Epitaxy Equation

This paper studies the cubic B-spline finite element approximation of an optimal control problem governed by the thin film epitaxy equation. The state and co-state variables are approximated by cubic B-spline finite elements, while the control variable is approximated by piecewise constant functions. The backward Euler scheme is employed for the time discretization. We derive some a priori error estimates for both the control and state variables. Numerical experiments are performed to verify the theoretical results.