$L^{\infty}$ Convergence of Conforming Finite Elements for the Biharmonic Equation

Abstract

The paper considers the $L^{\infty}$ convergence for conforming finite elements, such as Argyris element, Bell element and Bogner-Fox-Schmit element, solving the boundary value problem of the biharmonic equation. The nearly optimal order $L^{\infty}$ estimates are given.