Convergence of adaptive nonconforming finite element method for Stokes optimal control problems
发布时间：2024-10-25
点击次数：
- 所属单位：
- 理学院
- 发表刊物：
- JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
- 关键字：
- Optimal control problem Stokes equations Control constraints Adaptive nonconforming finite element method Convergence and quasi-optimality
- 摘要：
- 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 P1/P0 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
- 合写作者：
- 龚伟,严宁宁
- 第一作者：
- 沈玥
- 论文类型：
- 期刊论文
- 卷号：
- 412
- ISSN号：
- 0377-0427
- 是否译文：
- 否
- 发表时间：
- 2022-10-01