This study introduces Stackelberg-Nash equilibrium to neoclassical growth theory. It attempts make economic theory more robust in modelling the complexity of market structures. The model is constructed within framework Solow-Uzawa two-sector model. economy composed two sectors. final goods sector same as Solow one-sector which characterized by perfect competition. consumer Uzawa but Stackelberg...

In this paper we proposed a modified Lagrangian functional for obstacle problem, investigated its properties. Then we construct Uzawa method for finding a saddle point, proved the convergence theorems. Some numerical examples are provided.

A mixed nite element formulation for eeciently computing the velocity eld for uid ows in porous media is presented. Raviart Thomas (RT 0) and Brezzi Douglas Marini (BDM 1) spaces of lowest order are considered and compared both on analytic and realistic test cases. The BDM 1 space proves to be preferable to the simpler RT 0 with respect to CPU time and memory storage, if a xed accuracy is requi...

This paper proposes some nonlinear Uzawa methods for solving linear and nonlinear saddle-point problems. A nonlinear inexact Uzawa algorithm is first introduced for linear saddlepoint problems. Two different PCG techniques are allowed in the inner and outer iterations of the algorithm. This algorithm is then extended for a class of nonlinear saddle-point problems arising from some convex optimi...

Funding information China Scholarship Council (CSC), NDNS+PhD travel grant, DGA (Grupo consolidado PDIE), Grant/Award Number: FEDER/MCYT Projects MTM2013-40842-P, European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie, Grant/Award Number: 705402, POROSOS. Summary A poroelastic saturated medium can be modeled by means of Biot’s theory of consolidation. I...

Using an inexact Uzawa algorithm at the continuous level, we study the convergence of multilevel algorithms for solving saddle-point problems. The discrete stability Ladyshenskaya-Babušca-Brezzi (LBB) condition does not have to be satisfied. The algorithms are based on the existence of a multilevel sequence of nested approximation spaces for the constrained variable. The main idea is to maintai...

Recently, there have been many studies on solving different kinds of fuzzy equations. In this paper, the solution of a trapezoidal fully fuzzy linear system (FFLS) is studied. Uzawa approach, which is a popular iterative technique for saddle point problems, is considered for solving such FFLSs. In our Uzawa approach, it is possible to compute the solution of a fuzzy system using various relaxat...

We consider symmetric saddle point matrices. We analyze block preconditioners based on the knowledge of a good approximation for both the top left block and the Schur complement resulting from its elimination. We obtain bounds on the eigenvalues of the preconditioned matrix that depend only of the quality of these approximations, as measured by the related condition numbers. Our analysis applie...

A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur complement system that arises by eliminating the velocity. Each of the arising finite element problems...