Author(s)

Yanwei Li

School of Mathematics and Statistics, Shandong Normal University, Jinan, China.

In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretization of the control variable, we build up the virtual element discrete scheme of the optimal control problem and derive the discrete first order optimality system. A priori error estimates for the state, adjoint state and control variables in L² and H¹ norm are derived. The theoretical findings are illustrated by the numerical experiments.

Virtual Element Method, Optimal Control Problem, Brinkman Equations, A Priori Error Estimate

Li, Y. (2023) Virtual Element Discretization of Optimal Control Problem Governed by Brinkman Equations. Engineering, 15, 114-133. doi: 10.4236/eng.2023.152010.