A finite element approximation of the Stokes equations under a certain nonlinear boundary condition, namely, the slip or leak boundary condition of friction type, is considered. We propose an approximate problem formulated by a variational inequality, prove an existence and uniqueness result, present an error estimate, and discuss a numerical realization using an iterative Uzawa-type method. Se...

In optimal growth models, positive time preferences, i.e. people systematically discount utility derived from future consumption, is taken for granted [Olson and Bailey (1981)]. In addition, a further modeling of time preferences by Uzawa (1968), where the time preference is an increasing function of current utility, has been increasingly used in growth and asset accumulation models. See Obstfe...

In this paper a stabilizing augmented Lagrangian technique for the Stokes equations is studied. The method is consistent and hence does not change the continuous solution. We show that this stabilization improves the well-posedness of the continuous problem for small values of the viscosity coefficient. We analyze the influence of this stabilization on the accuracy of the finite element solutio...

Analysis and theoretical comparison between several fixed point strategies and Uzawa algorithms (for classical and augmented Lagrangian) are performed to solve the so called Signorini problem with Coulomb friction without any regularization. Thanks to a formalism coming from convex analysis, some new fixed point strategies are presented and compared to already known methods. The analysis is fir...

We consider the Uzawa method to solve the stationary Stokes equations discretized with stable finite elements. An iteration step consists of a velocity update un+1 involving the (augmented Lagrangian) operator −ν − ρ∇div with ρ ≥ 0, followed by the pressure update pn+1 = p − ανdiv un+1, the so-called Richardson update. We prove that the inf-sup constant β satisfies β ≤ 1 and that, if σ = 1 + ρν...

This paper studies the effect of endogenous discounting on distribution wealth in a Bewley–Huggett economy with an exogenous borrowing constraint. We introduce Koopmans–Uzawa–Epstein time preferences benchmark model Achdou et al. (2022) and investigate implications saving behaviour across different classes. The results highlight self-reinforcing redistribution mechanism, through which can lead ...