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Antonietti, P.F., Da Veiga, L.B., Scacchi, S. and Verani, M. (2016) A C¹ Virtual Element Method for the Cahn-Hilliard Equation with Polygonal Meshes. SIAM Journal on Numerical Analysis, 54, 34-56.
https://doi.org/10.1137/15M1008117

has been cited by the following article:

• TITLE: A Priori Error Analysis for NCVEM Discretization of Elliptic Optimal Control Problem

  AUTHORS: Shiying Wang, Shuo Liu

  KEYWORDS: Nonconforming Virtual Element Method, Optimal Control Problem, a Priori Error Estimate

  JOURNAL NAME: Engineering, Vol.16 No.4, April 30, 2024

  ABSTRACT: In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H1 and L2 norms. Finally, some numerical experiments are carried out to support the theoretical results.