首页|Convergence of adaptive nonconforming finite element method for Stokes optimal control problems
Convergence of adaptive nonconforming finite element method for Stokes optimal control problems
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NSTL
Elsevier
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.
Optimal control problemStokes equationsControl constraintsAdaptive nonconforming finite element methodConvergence and quasi-optimalitySTATIONARY STOKESERROR ANALYSISEQUATIONSDISCRETIZATION
NSTL
Elsevier
