A Nonconforming Finite Element Method for Fourth Order Curl Equations in R^3
Numerical Analysis
2010-02-02 v1
Abstract
In this paper we present a nonconforming finite element method for solving fourth order curl equations in three dimensions arising from magnetohydrodynamics models. We show that the method has an optimal error estimate for a model problem involving both curl^2 and curl^4 operators. The element has a very small number of degrees of freedom and it imposes the inter-element continuity along the tangential direction which is appropriate for the approximation of magnetic fields. We also provide explicit formulae of basis functions for this element.
Cite
@article{arxiv.1002.0131,
title = {A Nonconforming Finite Element Method for Fourth Order Curl Equations in R^3},
author = {Bin Zheng and Qiya Hu and Jinchao Xu},
journal= {arXiv preprint arXiv:1002.0131},
year = {2010}
}
Comments
16 pages, submitted