Conforming/non-conforming mixed finite element methods for optimal control of velocity-vorticity-pressure formulation for the Oseen problem with variable viscosity

IF 2.5 2区 数学 Q1 MATHEMATICS, APPLIED
Harpal Singh, Arbaz Khan
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引用次数: 0

Abstract

This work examines the distributed optimal control of generalized Oseen equations with non-constant viscosity and no-slip boundary conditions. We propose and analyze a new conforming augmented mixed finite element method and a discontinuous Galerkin (DG) scheme for the model written in velocity-vorticity-pressure formulation. The continuous formulation, which incorporates least-squares terms from both the constitutive equation and the incompressibility condition, is well-posed under certain assumptions on the viscosity parameter. The CG method is divergence-conforming and suits any Stokes inf-sup stable velocity-pressure finite element pair, while a generic discrete space approximates vorticity. The DG scheme employs a stabilization technique. We use two different approaches for the control approximation: a variational discretization and approximation through piecewise constant elements. We establish optimal a priori error estimates and residual-based a posteriori error estimates for both the proposed schemes. Finally, we provide numerical experiments to validate the theoretical estimates and showcase the performance and effectiveness of proposed schemes.
变黏度osee问题速度-涡度-压力公式优化控制的符合/不符合混合有限元方法
本文研究了具有非恒定粘度和无滑移边界条件的广义Oseen方程的分布最优控制。针对速度-涡度-压力模型,提出并分析了一种新的增广混合有限元法和不连续伽辽金格式。在粘性参数的某些假设下,结合了本构方程和不可压缩条件的最小二乘项的连续公式得到了良好的定态。CG方法是散度符合的,适用于任何Stokes -sup稳定速度-压力有限元副,而一般离散空间近似于涡量。DG方案采用了一种稳定技术。我们使用两种不同的方法来逼近控制:变分离散化和分段常数元逼近。我们建立了最优的先验误差估计和基于残差的后验误差估计。最后,我们提供了数值实验来验证理论估计,并展示了所提出方案的性能和有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Computers & Mathematics with Applications
Computers & Mathematics with Applications 工程技术-计算机:跨学科应用
CiteScore
5.10
自引率
10.30%
发文量
396
审稿时长
9.9 weeks
期刊介绍: Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).
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