Error analysis for the finite element approximations of Dirichlet parabolic boundary control problem with measure data

Shakya, P (2024) Error analysis for the finite element approximations of Dirichlet parabolic boundary control problem with measure data. In: Journal of Mathematical Analysis and Applications, 534 (2).

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Abstract

This article investigates the convergence analysis of finite element method for Dirichlet boundary control problem governed by parabolic equation with measure data. The presence of measure data in the source term and Dirichlet boundary control lead the solution of the state equation to have low regularity, which creates a challenging task for the error analysis. We prove the existence, uniqueness and regularity results of the solution to the control problem. For the discretization of the state and adjoint variables, we employ continuous piecewise linear polynomials while the control variable is approximated by piecewise constant functions. The backward Euler technique provides the foundation for the temporal discretization. For the completely discrete optimal control problem, a priori error bounds for the state variable in the L2(0,T;L2(Ω))-norm and for the control variable in the L2(0,T;L2(�Ω))-norm are derived. Numerical experiment is performed to validate our theoretical analysis. © 2024 Elsevier Inc.

Item Type:	Journal Article
Publication:	Journal of Mathematical Analysis and Applications
Publisher:	Academic Press Inc.
Additional Information:	The copyright for this article belongs to author
Department/Centre:	Others
Date Deposited:	01 Mar 2024 06:09
Last Modified:	01 Mar 2024 06:09
URI:	https://eprints.iisc.ac.in/id/eprint/83867

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