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Title: Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems
Authors: Gong, W
Li, B 
Issue Date: Oct-2020
Source: IMA journal of numerical analysis, Oct. 2020, v. 40, no. 4, p. 2898-2939
Abstract: The parabolic Dirichlet boundary control problem and its finite element discretization are considered in convex polygonal and polyhedral domains. We improve the existing results on the regularity of the solutions by establishing and utilizing the maximal Lp-regularity of parabolic equations under inhomogeneous Dirichlet boundary conditions. Based on the proved regularity of the solutions, we prove O(h1−1/q0−ϵ) convergence for the semidiscrete finite element solutions for some q0>2⁠, with q0 depending on the maximal interior angle at the corners and edges of the domain and ϵ being a positive number that can be arbitrarily small.
Keywords: Dirichlet boundary control
Parabolic equation
Finite element method
Maximal Lp-regularity
Publisher: Oxford University Press
Journal: IMA journal of numerical analysis 
ISSN: 0272-4979
EISSN: 1464-3642
DOI: 10.1093/imanum/drz029
Rights: © The Author(s) 2019. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Wei Gong, Buyang Li, Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems, IMA Journal of Numerical Analysis, Volume 40, Issue 4, October 2020, Pages 2898–2939 is available online at: https://doi.org/10.1093/imanum/drz029
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