A nonconforming finite element method for fourth order curl equations in ℝ³

Zheng, Bin; Hu, Qiya; Xu, Jinchao

doi:10.1090/S0025-5718-2011-02480-4

A nonconforming finite element method for fourth order curl equations in $\mathbb {R}^3$
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by Bin Zheng, Qiya Hu and Jinchao Xu PDF

Math. Comp. 80 (2011), 1871-1886 Request permission

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 $(\nabla \times )^2$ and $(\nabla \times )^4$ 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.

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