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 study the homogenization problem for a convection-diffusion equation in a periodic porous medium in the presence of chemical reaction on the pores surface. Mathematically this model is described in terms of a solution to a system of convection-diffusion equation in the medium and ordinary differential equation defined on the pores surface. These equations are coupled through the boundary con...

This paper deals with the analysis of different realizations regarding groundwater pollution. The groundwater behaviour can be implemented using a mixture of diffusion and convection equations. The analysis of the convection diffusion equation is also interesting for other research areas, for example biology, chemistry and the stock market. The first part will deal with the derivation of the re...

A nonstiff additive semi-implicit third-order Runge-Kutta scheme suitable for integration of convection-diffusion-reaction equations with few diffusion dominated species is presented in this article. This scheme permits larger time steps than those required by explicit schemes and uses only one implicit stage and two explicit stages. The stability domain is analyzed and tests are carried out fo...

Abstract. We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [7, 8] and the dependence of various constants upon the diffusion parameter is characterized. Error estimates...

A localized axial Green’s function method for convection-diffusion equations is proposed, which is a unique and original one for general cases of partial differential equations including elliptic boundary value problems and the steady Stokes flows. The salient feature of the method is that only one-dimensional Green’s functions for the axially split differential operators are used to solve the ...

This paper deals with the principle of groundwater pollution. The basic equation for pollution distribution is the diffusion equation. In the natural but also economical science different kinds of this equation are used. This work focuses on the convection-diffusion equation. Using this equation the diffusive behavior of the pollution influenced by a velocity field is described. Several approac...