Capacity of the Adini element for biharmonic equations

Abstract

This paper is devoted to the convergence analysis of the Adini element scheme for the fourth order problem in arbitrary dimension. We prove that, the Adini element scheme is $\mathcal{O}(h^2)$ order convergent in energy norm provided the exact solution is in $H^4$, and the convergence rate in $L^2$ norm can not be nontrivially higher than $\mathcal{O}(h^2)$ order. Numerical verifications are presented.