Singularities and regularity of stationary Stokes and Navier-Stokes equations on polygonal domains and their treatments

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.

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Geometric Singularities of the Poisson’s Equation in a Non-Smooth Domain with Applications of Weighted Sobolev Spaces

Anjam¹

2020

ijaa

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Singularities and regularity of stationary Stokes and Navier-Stokes equations on polygonal domains and their treatments

Cited by 4 publications

References 58 publications

A Finite Element Model for the Analysis of Seepage Flow of Water Under Concrete Dams

A Finite Element Model for the Analysis of Seepage Flow of Water Under Concrete Dams

An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner Singularities

Geometric Singularities of the Poisson’s Equation in a Non-Smooth Domain with Applications of Weighted Sobolev Spaces

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