A low order nonconforming anisotropic finite element approximation to parabolic problem

Ω fvdxdy. There have been a lot of work related to the finite element approximation to problem (1) in the framework of both semidiscrete and fully discrete schemes. For example, some superconvergence properties of conforming linear finite element (FE) were obtained by V. Thomeé with necessary help of Ritz projection and Lin Qun with a new analysis form, i.e., an analysis for the “short side” in the FE-right triangle plus the sharp integral estimates of the “hypotenuse”, rather than using the Ritz projection. The superconvergences of semidiscrete and fully discrete schemes of biquadratic element were studied by Lin and Pan, and X. Q. Liu with the same