NURBS-enhanced maximum-entropy schemes

In this paper, we combine high order local maximum-entropy schemes (HOLMES) with the integration framework developed in the NURBS-enhanced finite element method (NEFEM). We focus on the two-dimensional case where, given a domain described by some NURBS curves, a meshless formulation based on the HOLMES approximants is employed for the discretization and, at the same time, the geometric fidelity given by the NURBS boundary is preserved thanks to the NEFEM integration. Since HOLMES basis functions are not interpolatory on the boundary, different techniques are considered for the imposition of essential boundary conditions. The efficiency and the accuracy of the proposed methodology are confirmed with supportive numerical examples.