A Nonconforming Finite Element Method for Fourth Order Curl Equations in R^3

Details A Nonconforming Finite Element Method for Fourth Order Curl Equations in R^3 A Nonconforming Finite Element Method for Fourth Order Curl Equations in R^3

2010-01-31

arxiv.org/abs/1002.0131v1

Mathematics

Numerical Analysis

16 pages, submitted

Scientific paper

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.

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