Anisotropic Variable Grid Carey Parabolic Triangular Finite Element Method

The classical finite element approximation theory relies on the regular or quasi-uniform assumption, i.e., there exists a constant C >0, such that forall element where h_K and ρ_K are the diameters of K and the biggest circle contained in Krespectively. However, with the development of application of finite elements, above conditions have been severe restrictive factors. At the same time, the solution of some problems may have anisotropic behavior. That means that the solution varies significantly only in certain direction. In such that case it is an obvious idea to reflect this anisotropy in the discretization by using anisotropic meshes with a small mesh size in the direction of the rapid variation of the solution and a large mesh size in the perpendicular direction.In this paper, the main contents are the anisotropic nonconforming finiteelement methods with moving grid for parabolic problem. By using Careyelement's special properties and combining with the moving grid techniques, the parabolic problems are studied. At the same time, by using the Rieszprojection, the optimal error estimates in energy norm and L~2-norm ofare obtained. Thus the classical regularity or quasi-uniform assumption is not necessarily for some elements and the anisotropic finite elements extends the application scope of the anisotropic finite elements is extended (especially the nonconforming ones)...