Convergence of adaptive nonconforming finite element method for Stokes optimal control problems
Shen, Yue 1Gong, Wei 2Yan, Ningning2
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作者信息
1. Xian Univ Architecture & Technol
2. Chinese Acad Sci
折叠
Abstract
This paper aims at proving the convergence and quasi-optimality of an adaptive nonconforming finite element method for Stokes distributed control problems with pointwise control constraints. Nonconforming P-1/P-0 pair (Crouzeix-Raviart elements) and variational discretization are used to approximate the state equation and the control variable, respectively. A posteriori error estimates with upper and lower bounds are first derived for the state and adjoint variables. Then we prove the contraction property for the sum of the energy error of the state and adjoint state and the scaled error estimator on two consecutive adaptive meshes. The resulting linear convergence is finally used to show the quasi-optimal convergence rate of the adaptive algorithm. Additionally, some numerical results are provided to support our theoretical analysis. (c) 2022 Elsevier B.V. All rights reserved.
Key words
Optimal control problem/Stokes equations/Control constraints/Adaptive nonconforming finite element method/Convergence and quasi-optimality/STATIONARY STOKES/ERROR ANALYSIS/EQUATIONS/DISCRETIZATION
NSTL
Elsevier