Convergence and Superconvergence of Hermite Bicubic Element for Eigenvalue Problem of the Biharmonic Equation

Abstract

In this paper,we discuss the convergence and superconvergence for eigenvalue problem of the biharmonic equation by using the Hermite bicubic element. Based on asymptotic error expansions and interpolation postprocessing, we gain the following estimation: $$0 \le \bar{\lambda}_h - \lambda \le C_\epsilon h^{8-\epsilon}$$ where $\epsilon＞0$ is an arbitrary small positive number and $C_\epsilon ＞0$ is a constant.