Error estimates for a bubble-enriched $C^0$ interior penalty method to a reduced state constrained elliptic optimal control problem

Abstract

In this article, we study a bubble-enriched C^y0 interior penalty method for the elliptic optimal control problem with pointwise control constraints. We have used the strategy of converting the control constrained optimization problem into a state constrained optimization problem by removing the control variable. The convergence behavior is obtained in H² -like energy norm. We present numerical tests to validate our theoretical results.