Workshop Singularly Perturbed Problems
Talks & Slides
On Recent Experience With Discretizations of Convection-Diffusion Equations
Solutions of convection-dominated convection-diffusion equations possess layers which generally cannot be resolved by standard (reasonable) meshes in two and three dimensions. Consequently, it is not possible to compute meaningful solutions with standard discretizations. The use of special discretizations, like stabilized finite element methods, becomes necessary. There are many proposals of such discretizations, but there is not yet a discretization which can be generally recommended. In addition, comprehensive numerical studies which include numerous discretizations are too rare.
In applications, aspects like spurious oscillations, position and smearing of layers, and efficiency are important motivations for choosing a discretization. With respect to these criteria, we carried out numerical studies for steady-state and time-dependent convection-diffusion equations with a number of discretizations, including finite element schemes, finite volume methods, and finite difference schemes. The talk will present characteristic results obtained in these studies and the most important conclusions.