Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems
2019 ◽
Vol 40
(4)
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pp. 2898-2939
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Keyword(s):
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 $L^p$-regularity of parabolic equations under inhomogeneous Dirichlet boundary conditions. Based on the proved regularity of the solutions, we prove ${\mathcal O}(h^{1-1/q_0-\epsilon })$ convergence for the semidiscrete finite element solutions for some $q_0>2$, with $q_0$ depending on the maximal interior angle at the corners and edges of the domain and $\epsilon$ being a positive number that can be arbitrarily small.
2020 ◽
Vol 20
(4)
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pp. 827-843
1983 ◽
Vol 21
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pp. 41-67
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Vol 49
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pp. 984-1014
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pp. 637-644
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2018 ◽
Vol 39
(4)
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pp. 1985-2015
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Vol 54
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pp. 2526-2552
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Vol 40
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pp. 800-800
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Vol 129
(4)
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pp. 723-748
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Vol 41
(4)
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pp. 681-715
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