The characteristic finite difference streamline diffusion method for convection-dominated diffusion problems

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

Adaptive Streamline Diffusion Finite Element Methods for Stationary Convection-diffusion Problems

Adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed. The underlying discretization scheme is the Shock-capturing Streamline Diffusion method. The adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed. A priori error estimates ar...

Robust DPG Method for Convection-Dominated Diffusion Problems

Explicit Finite Difference Method For Convection-Diffusion Equations

In this paper, we present an integral form of convection-diffusion equation. Then a class of alternating group explicit finite difference method (AGE) is constructed based on several asymmetric schemes. The AGE method is unconditionally stable and has the property of parallelism. Results of numerical examples show the AGE method is of high accuracy.

The Discrete Duality Finite Volume Method for Convection-diffusion Problems

In this paper we extend the Discrete Duality Finite Volume (DDFV) formulation to the steady convection-diffusion equation. The discrete gradients defined in DDFV are used to define a cellbased gradient for the control volumes of both the primal and dual meshes, in order to achieve a higher-order accurate numerical flux for the convection term. A priori analysis is carried out to show convergenc...