The lower bound of the error estimate in the L2 norm for the Adini element of the biharmonic equation

2012/11/20 by Jun Hu, Hu, Jun, Zhong‐Ci Shi +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1211.4677

openalex publication_date 2012/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the L² norm error estimate of the Adini element for the biharmonic equation. Surprisingly, a lower bound is established which proves that the L² norm convergence rate can not be higher than that in the energy norm. This proves the conjecture of [Lascaux and Lesaint, Some nonconforming finite elements for the plate bending problem, RAIRO Anal. Numer. 9 (1975), pp. 9--53.] that the convergence rates in both L² and H¹ norms can not be higher than that in the energy norm for this element.

Citations

• The Lower Bounds for Eigenvalues of Elliptic Operators --By Nonconforming Finite Element Methods

Related

• Capacity of the Adini element for biharmonic equations
• On the Penalty term for the Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
• 3D H²-nonconforming tetrahedral finite elements for the biharmonic equation
• The stabilizer-free weak Galerkin finite element method for the Biharmonic equation using polynomials of reduced order
• The Adini finite element on locally refined meshes