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Beirão da Veiga, L., Brezzi, F., Cangiani, A., et al. (2013) Basic Principles of Virtual Element Methods. Mathematical Models and Methods in Applied Sciences, 23, 199-214.
https://doi.org/10.1142/S0218202512500492

has been cited by the following article:

• TITLE: Virtual Element Discretization of Optimal Control Problem Governed by Brinkman Equations

  AUTHORS: Yanwei Li

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

  JOURNAL NAME: Engineering, Vol.15 No.2, February 24, 2023

  ABSTRACT: 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.