The Anisotropic Finite Element Methods For Fourth Order Parabolic Equations

In this paper, the nonconforming ACM element is applied to one fourth order parabolic eqution on anisotropic meshes. The supercolse result is obtained in semidiscrete scheme by higher accuracy analytical technique. At the same time, the global superconvergence result is also provided through a properly postprocessing technique. Then, more accurate exptrapolation is proved based on asymptotic expansion of the error. Next, the bicubic Hermite element is applied to another fourth order parabolic equation on anisotropic meshes, and superclose result is obtained.