Skew-symmetric iteration methods for solving stationary problem of convection-diffusion with a small parameter at the highest derivative (Q1390384)

This article is concerned with stationary convection-dominated (i.e., singularly perturbed) convection-diffusion equations, together with the incompressibility condition \(\text{div }U= 0\) and Dirichlet boundary conditions. Incorporating the incompressibility condition into the equation, it is brought into a ``symmetric'' form, i.e., its left-hand side can be written as a sum of a symmetric (diffusion) and a skew-symmetric (convection) operator. By use of central differences, these symmetry properties are carried over to the resulting discrete system. This facilitates special iteration methods not requiring a diagonally dominant matrix, which are therefore well suited for convection-dominated problems. Numerical examples illustrate the method.