Anisotropic Approximations To Stokes Eigenvalue Prolems And Variational Inequality With Curvature Obstacle

The paper focuses on approximations of anisotropic nonconforming Crouzeix-Raviart element for Stokes eigenvalue problem and Morley's element for a fourth order vari-ational inequality with curvature obstacle on anisotropic meshes. The aims of this paper are to derive the optimal error estimates of eigenpairs, i.e. the optimal error estimate of eigenvalues, and the new error estimates of velocity, pressure including the L~2 - norm and energy norm, respectively, in which the L~2 - norm estimate of velocity on anisotropic meshes has not ever been seen in the precious literature. At the same time, the superclose estimate and superconvergence are also presented. For Morley's triangular anisotropic nonconforming element we obtains the optimal error estimate of O(h) to variational inequality with curvature obstacle. The results of this paper show that the classical regularity condition or quasi-uniform assumption on the triangula-tion meshes is not necessary to the finite element analysis and thus the scope of finite element application is extended.