Using a technique for constructing analytic expressions for discrete solutions to the convection-diffusion equation, we examine and characterize the effects of upwinding strategies on solution quality. In particular, for grid-aligned flow and discretization based on bilinear finite elements with streamline upwinding, we show precisely how the amount of upwinding included in the discrete operato...

Random walks are developed to approximate the solutions of multiscaling, fractional-order, anomalous diffusion equations. The essential elements of the diffusion are described by the matrix-order scaling indexes and the mixing measure, which describes the diffusion coefficient in every direction. Two forms of the governing equation (also called the multiscaling fractional diffusion equation), b...

We investigate the optimal accuracy of the streamline diffusion finite element method applied to convection–dominated problems. For linear/bilinear elements the theoretical order of convergence given in the literature is either O(h3/2) for quasi–uniform meshes or O(h2) for some uniform meshes. The determination of the optimal order in general was an open problem. By studying a special type of m...

In this paper we analyze local properties of the Continuous Interior Penalty (CIP) Method for a model convection-dominated singularly perturbed convection-diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows that locally, the CIP method is comparable to the Streamline Diffusion (SD) or t...

— We consider the discretization of linear, nonstationary, convection-dominated, convection-diffusion Systems by the streamline diffusion finite element method and give local error estimâtes in the energy norm for both linear scalar équations in arbitrary dimensions and for Systems in one space dimension. For piecewise linear shape functions in time-space that are continuons in space and discon...