Harbir Antil, Rohit Khandelwal, Umarkhon Rakhimov, A discontinuous Galerkin method for optimal control of the obstacle problem

Full Text: PDF
DOI: 10.23952/jano.7.2025.3.09
Volume 7, Issue 3, 1 December 2025, Pages 459-477

Abstract. This paper provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty discontinuous Galerkin method. The main proofs are based on the improved $L^2$ -error estimates for the obstacle problem, the discrete maximum principle, and a well-known quadratic growth condition. The standard (restrictive) assumptions on mesh are not assumed here.

How to Cite this Article:
H. Antil, R. Khandelwal, U. Rakhimov, A discontinuous Galerkin method for optimal control of the obstacle problem, J. Appl. Numer. Optim. 7 (2025), 459-477.