Some High Accuracy Analysises For Evolution Equations On Anisotropic Meshes

A class of low order nonconforming elements are applied to parabolic equation on anisotropic meshes. The semidiscrete scheme and fully discrete shceme are discussed respectively and the superclose results are obtained based on higher accuracy analytical technique. At the same time, the global superconvergence result is also provided through a proper postprocessing technique. Meanwhile, the similar results are obtained for hyperbolic equation under semidiscrete shceme with above elements. On the other hand, the superclose property of biquadratic element for parabolic equation under fully discrete schemes are discussed and the ideal results are gained.