Capacity of the Adini element for biharmonic equations

Jun Hu; Xueqin Yang; Shuo Zhang

Capacity of the Adini element for biharmonic equations

Numerical Analysis 2015-05-12 v1

Authors: Jun Hu , Xueqin Yang , Shuo Zhang

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.

Keywords

Adini element biharmonic equation convergence analysis fourth order problem energy norm L^2 norm arbitrary dimension

Cite

@article{arxiv.1505.02332,
  title  = {Capacity of the Adini element for biharmonic equations},
  author = {Jun Hu and Xueqin Yang and Shuo Zhang},
  journal= {arXiv preprint arXiv:1505.02332},
  year   = {2015}
}

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