An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner Singularities. (9th June 2021)

• Record Type: Journal Article
• Authors: Pyo, Jae-Hong; Jang, Deok-Kyu
• Other Names: Qin Xiaolong Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-06-09
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/5592982
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : The Uzawa method is an iterative approach to find approximated solutions to the Stokes equations. This method solves velocity variables involving augmented Lagrangian operator and then updates pressure variable by Richardson update. In this paper, we construct a new version of the Uzawa method to find optimal numerical solutions of the Stokes equations including corner singularities. The proposed method is based on the dual singular function method which was developed for elliptic boundary value problems. We estimate the solvability of the proposed formulation and special orthogonality form for two singular functions. Numerical convergence tests are presented to verify our assertion.