NURBS-enhanced finite element method (NEFEM) on quadrilateral meshes

This paper formulates quadrilateral elements for the NURBS-enhanced finite element method (NEFEM). The objective is to extend the application of NEFEM to problems where the use of quadrilateral elements is preferred. By leveraging a mapping, between reference and physical spaces, that encapsulates the exact boundary representation of the domain, a tight integration with computer aided design (CAD) systems is achieved. The contribution of this work is an enhanced quadrilateral finite element that incorporates the exact CAD geometry purely from the boundary representation (B-rep) from CAD and without the need for a whole volume representation (V-rep) as a NURBS entity. Numerical examples involving heat transfer and linear elastic problems are used to numerically demonstrate the optimal convergence properties of the method under mesh refinement.