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...

In this paper, we present an Uzawa-based heuristic that is adapted to some type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale independent subsystems, though linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, ...

Human capital, in the form of embodied knowledge or skills, is under threat of automation. To examine the effect of it on a macroeconomy, I develop the Uzawa-Lucas model in which the accumulation of human capital follows the stochastic process. With two equality constraints, the closed-form solution gets obtainable. It shows that increase in uncertainty about the human capital accumulation redu...

This article presents a robust and efficient methodology to study three-dimensional thermoelastic contact problems under orthotropic friction conditions, including the effects of non-linear thermal conductance convective boundary conditions at interstitial zone. The proposed considers element method compute thermomechanical influence coefficients an augmented Lagrangian formulation ensure fulfi...

The paper proposes a new test of endogenous vs. exogenous growth theories based on the Granger-causality methodology and applies it to a panel of 20 OECD countries. The test yields divergent evidence with respect to physical and human capital. For physical capital, the test results favor Solow-type exogenous growth theory over AK-type endogenous growth models. On the other hand, the test result...

Certain implicit time stepping procedures for the incompressible Stokes or Navier-Stokes equations lead to a singular-perturbed Stokes type problem at each type step. The paper presents a convergence analysis of a geometric multigrid solver for the system of linear algebraic equations resulting from the disretization of the problem using a finite element method. Several smoothing iterative meth...

The preconditioner for parameterized inexact Uzawa methods have been used to solve some indefinite saddle point problems. Firstly, we modify the preconditioner by making it more generalized, then we use theoretical analyses to show that the iteration method converges under certain conditions. Moreover, we discuss the optimal parameter and matrices based on these conditions. Finally, we propose ...

In this paper, we seek a solution to linear inverse problems arising in image restoration in terms of a recently posed optimization problem which combines total variation minimization and wavelet-thresholding ideas. The resulting nonlinear programming task is solved via a dual Uzawa method in its general form, leading to an efficient and general algorithm which allows for very good structure-pr...