The Schur complement of a model problem is considered as a preconditioner for the Uzawa type schemes for the generalized Stokes problem (the Stokes problem with the additional term αu in the motion equation). The implementation of the preconditioned method requires for each iteration only one extra solution of the Poisson equation with Neumann boundary conditions. For a wide class of 2D and 3D ...

In this paper we consider a mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with complementarity constraints. Various stationary conditions for MPECs exist in literature due to different reformulations. We give a simple proof to the M-stationary condition and show that it is sufficient for global or local optimality under some MPEC generalized conve...

Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizatiom a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the dkretization. In this paper we compare the performance of four such methods, namely variants of the Uzawa, preconditioned conjugate gradient, precondi...

We consider multigrid methods for discontinuous Galerkin (DG) H(div, Ω)-conforming discretizations of the Stokes equation. We first describe a simple Uzawa iteration for the solution of the Stokes problem, which requires a solution of a nearly incompressible linear elasticity problem on every iteration. Then, based on special subspace decompositions of H(div, Ω), as introduced in [J. Schöberl. ...

Investments in human capital are individual and collective choices carrying significant external effects. Educated parents friends accelerate our own accumulation. Skilled colleagues at work increase productivity. Sharing experiences with cultured people is gratifying by itself. We introduce externalities a stylized model à la Uzawa (1965) we find that growth can be no longer balanced the equil...

In this paper we generalize the approach in [5] and discuss an interface problem consisting of a non-linear partial differential equation in Ω ⊂ Rn (bounded, Lipschitz, n ≥ 2) and the Laplace equation in the unbounded exterior domain Ωc := R n\Ω̄ fulfilling some radiation condition, which are coupled by transmission conditions and Signorini conditions imposed on the interface. The interior pde i...

Numerous cross-sectional tests have been performed to evaluate the predictions of recent growth theories such as the Uzawa-Lucas growth model. In a series of papers and in his book, Jones (1995a, 1995b, 1997) has shifted the attention toward the time series predictions of endogenous growth models. By contrasting endogenous growth models with facts, one is frequently confronted with the predicti...