The Gauge-Uzawa Finite Element Method. Part I: The Navier-Stokes Equations

Fully Discrete Finite Element Approximation for the Stabilized Gauge-Uzawa Method to Solve the Boussinesq Equations

The stabilized Gauge-Uzawa method (SGUM), which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations o...

Optimal Error Estimate for Semi-discrete Gauge-uzawa Method for the Navier-stokes Equations

The gauge-Uzawa method which has been constructed in [11] is a projection type method to solve the evolution Navier-Stokes equations. The method overcomes many shortcomings of projection methods and displays superior numerical performance [11, 12, 15, 16]. However, we have obtained only suboptimal accuracy via the energy estimate in [11]. In this paper, we study semi-discrete gauge-Uzawa method...

A Convergent Adaptive Uzawa Finite Element Method for the Nonlinear Stokes Problem

Uzawa type algorithms for nonsymmetric saddle point problems

In this paper, we consider iterative algorithms of Uzawa type for solving linear nonsymmetric saddle point problems. Specifically, we consider systems, written as usual in block form, where the upper left block is an invertible linear operator with positive definite symmetric part. Such saddle point problems arise, for example, in certain finite element and finite difference discretizations of ...

Some Uzawa methods for steady incompressible Navier-Stokes equations discretized by mixed element methods

Numerical solutions of Navier-Stokes equations play fundamental roles in scientific computing and fluid mechanics. In this talk, I am going to present some Uzawa-type iterative methods for solving the steady incompressible Navier-Stokes equations discretized by mixed element methods. Compared with most existing iterative methods, these methods require no numerical solution of any saddle-point s...