Capacity of the Adini Element for Biharmonic Equations
Journal of Scientific Computing(2016)
摘要
This paper is devoted to the convergence analysis of the Adini element scheme for biharmonic equations in any dimension. In particular, a second order convergence in the energy norm is established provided that the exact solution is in H^4 . Surprisingly, it is proved that the convergence rate in the L^2 norm can not be nontrivially higher than 𝒪(h^2) order. The main ingredient for the analysis is a crucial structure of the Adini element space. Numerics are presented to demonstrate the theoretical results.
更多查看译文
关键词
Biharmonic equation,Adini element,Error estimate,Arbitrary dimension
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络