Standard (conforming) finite element approximations of convection-dominated convectiondiffusion problems often exhibit poor stability properties that manifest themselves as nonphysical oscillations polluting the numerical solution. Various techniques have been proposed for the stabilisation of finite element methods (FEMs) for convection-diffusion problems, such as the popular streamline upwind...

In the past several years, domain decomposition has been a very popular topic, partly motivated by the potential of parallelization. While a large body of theory and algorithms have been developed for model elliptic problems, they are only recently starting to be tested on realistic applications. In this paper, after a brief introduction and survey of the literature, we shall investigate the ap...

We present a multigrid method for the solution of convection diffusion equations that is based on the combination of recursive substructuring techniques and the discretization on hierarchical bases and generating systems. Robustness of the resulting method, at least for a variety of benchmark problems, is achieved by a partial elimination between certain "coarse grid unknowns". The choice of th...

We combine the finite element method with the Eulerian–Lagrangian Localized Adjoint Method (ELLAM) to solve the convection–diffusion equations that describe the kinematics of magnetohydrodynamic flows, i.e., the advection and diffusion of a magnetic field. Simulations of three two-dimensional test problems are presented and in each case we analyze the energy of the magnetic field as it evolves ...

The numerical solution of a parabolic convection diffusion equation with delay term is considered. This includes both variants, the initial value problem and the prehistory problem. Equations with a delay or memory term, often called integrodifferential problems, appear in different contexts of heat conduction in materials with memory, viscoelasticity and population models. This work concentrat...

Multigrid schemes based on high order compact discretization are developed for convection-diffusion problems. These multigrid schemes circumvent numerical oscillations and instability, while also yielding higher accuracy. These instabilities are typically exacerbated by the coarser grids in multigrid calculations. Our approach incorporates a 4th order compact formulation for the discretization,...

This paper aims to give the reader a summary of current understanding of the streamlinediffusion finite element method (SDFEM), as applied to linear steady-state convection-diffusion problems. Towards this end, we begin with a brief description of the nature of convectiondiffusion problems: the structure of their solutions will be examined, with special emphasis on the main phenomena of exponen...