On finite element approximation and stabilization methods for compressible viscous flows

This work is devoted to the numerical solution of the Navier–Stokes equations for compressible viscous fluids. Finite element approximations and stabilization techniques are addressed. We present methods to implement discontinuous approximations for the pressure and the density. An upwinding methodology is being investigated which combines the ideas behind the stream line Petrov–Galerkin method and the flux limiter methods aiming to introduce numerical diffusion only where it is necessary.     

Rule-based procedures in short-term electricity load forecasting

A short-term load-forecasting system has been developed to predictload demand for the Irish Electricity Supply Board from 1 to10 days in advance. Model output is acceptably accurate at mosttimes, but special days such as public holidays and the Easterweekend etc. require individual treatment. The basic model usedin everyday load forecasting is presented first, and specialdays when this model fails in accuracy are then examined andtreated separately using rule-based procedures. These proceduresare based on identified relationships between weather conditionsand prevailing daily load shapes. Comparisons are made betweenthe forecasts for these special days as given by the standardmodel and the ruled-based procedures.     

Kinetics of zinc(II) cloride extraction with tributyl phosphate

The equilibrium and rate of solvent extraction of zinc chloride complexes from HCl solutions into benzene solutions of tributyl phosphate (TBP) have been studied. The extracted species are discussed in the light of the results. The extraction was found to be first order with respect to both Zn(II) and TBP, and zero order for HCl. The rate-controlling steps are discussed and the rate constants for these reactions are calculated.     

Geometric quantization of topological gauge theories

We show that Abelian gauge theories in 2+1 space-time dimensions with the introduction of a topological Chern-Simons term can be quantized with the use of the symplectic formalism. The consistency of our results are verified by the agreement with the ones from the Dirac case.     

Optimal algebraic multilevel preconditioning for local refinement along a line

The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.