The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linea...

We introduce a simple method of analyzing the transitional dynamics of the Uzawa-Lucas endogenous growth model with human capital externalities. We use the value function approach to solve both the social planner’s optimization problem in the centralized economy and the representative agent’s optimization problem in the decentralized economy. The complexity of the Hamilton-Jacobi-Bellman equati...

We consider a generalized Stokes equation with problem parameters 0 (size of the reaction term) and >0 (size of the diffusion term). We apply a standard finite element method for discretization. The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point problem. We investigate a coupled multigrid method with Braess–Sarazin and Vanka-type smooth...

Abstract The main goal of this article is to discuss a numerical method for finding the best constant in a Sobolev type inequality considered by C. Sundberg, and originating from Operator Theory. To simplify the investigation, we reduce the original problem to a parameterized family of simpler problems, which are constrained optimization problems from Calculus of Variations. To decouple the var...

We present in this paper an iterative algorithm to solve constraint forces for haptic interactive simulation. The haptic forces are induced by interaction with guidance virtual fixtures having forbidden regions. In general, a haptic rendering based on an explicit formulation of the constraint forces (with virtual springs) can lead to severe numerical stability problems in case of hard constrain...

The small open economy model with incomplete asset markets features a steady-state that depends on initial conditions and equilibrium dynamics that possess a random walk component. A number of modifications to the standard model have been proposed to induce stationarity. This paper presents a quantitative comparison of these alternative approaches. Five different specifications are considered: ...

Based on the use of shell kinematics, a theoretical model is developed to predict time-dependent responses Saccharomyces cerevisiae yeasts. These cells are herein described as thin-walled shells with axisymmetrical shapes and, due their soft nature, finite strain range priori adopted. Accordingly, viscoelastic modeling assumed for cell-wall. An Ogden-type energy function used together creep-lik...