We give a self-contained presentation of our macroelement technique for verifying the stability of finite element discretizations of Navier-Stokes equations in the velocity-pressure formulation. The results are also presented in form suitable for the non-mathematical reader.

This paper is concerned with the one-dimensional stationary linear Wigner equation, a kinetic formulation of quantum mechanics. Specifically, we analyze the well-posedness of the boundary value problem on a slab of the phase-space with given inflow data for a discrete-velocity model. We find that the problem is uniquely solvable if zero is not a discrete velocity. Otherwise one obtains a differ...

In this paper we study the time dependent Stokes problem with some different boundary conditions. We establish a decoupled variational formulation into a system of velocity and a Poisson equation for the pressure. Hence, the velocity is approximated with curl conforming finite elements in space and Euler scheme in time and the pressure with standard continuous elements in space and Euler scheme...

In this paper we study the Stokes problem with some non standard boundary conditions. The variational formulation decouples into a system velocity and a Poisson equation for the pressure. The continuous and corresponding discrete system do not need an inf-sup condition. Hence, the velocity is approximated with curl conforming finite elements and the pressure with standard continuous elements. N...

This paper is concerned with the one-dimensional stationary linear Wigner equation, a kinetic formulation of quantum mechanics. Specii-cally, we analyze the well-posedness of the boundary value problem on a slab of the phase-space with given innow data for a discrete-velocity model. We nd that the problem is uniquely solvable if zero is not a discrete velocity. Otherwise one obtains a diierenti...

The paper deals with a numerical modelling of equiaxed microstructure formation during the solidification of two-component alloys. The basic enthalpy formulation was applied to model the solidification. The equiaxed grain size was dependent on the average cooling velocity at the moment when the liquid metal reaches the liquidus temperature. The experimentally determined dependence between grain...