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New vectorial
 H
 (curl) shape functions for the edge meshless method

New vectorial shape functions for the edge meshless method are introduced. The theory to develop these functions is based on Nedelec's elements of the first type in the H ( curl ; Ω ) space. The mathematical formulation to construct the shape functions is presented and the method's main characteristics in two dimensions are verified numerically. As a result, it is shown that the numerical solution is not corrupted by spurious modes and that the new shape functions are less dependent on edges distribution in the problem domain. Furthermore, it is possible to generate consistent approximations even when the length of the edges tends to zero.