Accepted

Convergence of adaptive edge finite element methods for H(curl)-elliptic problems

Liuqiang Zhong, Shi Shu, Long Chen, Jinchao Xu

Numerical Linear Algebra with Applications

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ABSTRACT:

 
The standard Adaptive Edge Finite Element Method (AEFEM),
using first/second family Nedelec edge elements with any order, for
the three dimensional H(curl)-elliptic problems with variable
coefficients is shown to be convergent for the sum of the energy error
and the scaled error estimator. The special treatment of the data
oscillation and the interior node property are removed from the
proof. Numerical experiments indicate that the adaptive meshes and the
associated numerical complexity are quasi-optimal.