Adaptive Finite Element Method for an Elliptic Optimal Control Problem with Integral State Constraints

doi:10.1007/s42967-024-00397-8

Abstract

Abstract: In this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with two different sets of constraints, namely (i) integral state constraint and integral control constraint; (ii) integral state constraint and pointwise control constraints. In the analysis, we have taken the approach of reducing the state-control constrained minimization problem into a state minimization problem obtained by eliminating the control variable. The reliability and efficiency of a posteriori error estimator are discussed. Numerical results are reported to illustrate the behavior of the error estimator.

Key words: Elliptic optimal control problem, Fourth-order variational inequality, Integral state constraints, Adaptive finite element method

CLC Number:

Pratibha Shakya, Kamana Porwal. Adaptive Finite Element Method for an Elliptic Optimal Control Problem with Integral State Constraints[J]. Communications on Applied Mathematics and Computation, 2026, 8(1): 1-40.

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References

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