A Nonconforming Finite Element Approximation for Optimal Control of an Obstacle Problem

Asha K. Dond 1 , Thirupathi Gudi 2 ,  and Neela Nataraj 3
  • 1 Department of Mathematics, Indian Institute of Technology Bombay, Mumbai 400076, India
  • 2 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
  • 3 Department of Mathematics, Indian Institute of Technology Bombay, Mumbai 400076, India
Asha K. Dond, Thirupathi Gudi and Neela Nataraj


The article deals with the analysis of a nonconforming finite element method for the discretization of optimization problems governed by variational inequalities. The state and adjoint variables are discretized using Crouzeix–Raviart nonconforming finite elements, and the control is discretized using a variational discretization approach. Error estimates have been established for the state and control variables. The results of numerical experiments are presented.

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