We consider a variational problem for three-dimensional (3D) classical lattice models, where the trial state is given by a uniform 2D product of local factors. Maximization of the variational partition function draws a self-consistent equation for the local factor. We propose a stable algorithm to solve the equation numerically when the variational function contains many degrees of freedom. Num...

The Gauge-Uzawa FEM is a new first order fully discrete projection method which combines advantages of both the Gauge and Uzawa methods within a variational framework. A time step consists of a sequence of d+1 Poisson problems, d being the space dimension, thereby avoiding both the incompressibility constraint as well as dealing with boundary tangential derivatives as in the Gauge Method. This ...

A. We construct optimal order multilevel preconditioners for interior-penalty discontinuous Galerkin (DG) finite element discretizations of three-dimensional (3D) anisotropic elliptic boundary-value problems. In this paper we extend the analysis of our approach, introduced earlier for 2D problems [20], to cover 3D problems. A specific assembling process is proposed which allows us to cha...

‎we consider nonconvex vector optimization problems with variable ordering structures in banach spaces‎. ‎under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...