Modified C0 interior penalty analysis for fourth order Dirichlet boundary control problem and a posteriori error estimates

Sudipto Chowdhury, Divay Garg and Ravina Shokeen

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 219, issue C, 185-211

Abstract: We revisit the L2 norm error estimate for the C0-interior penalty analysis of fourth order Dirichlet boundary control problem. The L2 norm error estimate for the optimal control is derived under reduced regularity assumption and this analysis can be carried out on any convex polygonal domain. Moreover, residual based a posteriori error bounds are derived for the optimal control, state and adjoint state variables under minimal regularity assumptions. The error estimator is shown to be reliable and locally efficient. The theoretical findings are illustrated by numerical experiments.

Keywords: Optimal control; C0-IP method; Dirichlet boundary control; A priori error estimates; A posteriori error estimates; Cahn-Hilliard boundary condition; Biharmonic equation; Finite element method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:219:y:2024:i:c:p:185-211

DOI: 10.1016/j.matcom.2023.12.025

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