An Extended Finite Element Method for 2D Edge Elements

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Abstract

A new eXtended Finite Element Method based on two-dimensional edge elements is presented and applied to solve the time-harmonic Maxwell equations in domains with cracks. Error analysis is performed and shows the method to be convergent with an order of at least $O(h^{1/2-\eta})$. The implementation of the method is discussed and numerical tests illustrate its performance.

Keywords:

Maxwell's equations domains with cracks XFEM singularities of solutions.
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