Numerical study of finite element methods for convection-diffusion problems (Q2730696)

Accuracy and numerical stability of three finite element schemes are thoroughly investigated in numerical experiments for convection-diffusion problems. The aim of this study is to develop robust and accurate solvers for computational fluid dynamics problems. Least-squares approach with standard and stabilized finite element methods is under consideration. The schemes are compared from the viewpoint of their approximation properties and sensitivity to the smoothness of the initial data in a wide range of the Péclet numbers. In particular, the correlation between the error of the method, the mesh size, and the Péclet number is studied for all three schemes. The results reveal new interesting properties of these finite element schemes, which can be useful for their further development.