An Error Analysis for the Finite Element Method Applied to Convection Diffusion Problems

摘要

This paper analyzes the finite element method applied to a convection diffusion model problem. Linear elements are used for the trial space. The error is measured in a norm closely related to the L sup P norm. When the test space is composed of linear elements with parabolic upwinding, the method is shown to be optimal when the input data is piecewise smooth -- a condition which is usually observed in practice. Without these smoothness assumptions, the method is shown to be non-optimal, even if the class of test spaces is extended to include any elements which have a shape independent of the mesh size. (Author)