Capacity of the Adini element for biharmonic equations
Provides theoretical convergence guarantees for the Adini element in higher dimensions, benefiting numerical analysts working on finite element methods for fourth-order problems.
This paper analyzes the convergence of the Adini element for biharmonic equations in arbitrary dimensions, proving second-order convergence in the energy norm for H^4 solutions and showing the L^2 convergence rate cannot exceed second order.
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.