NURBS based least‐squares finite element methods for fluid and solid mechanics

This contribution investigates the performance of a least‐squares finite element method based on non‐uniform rational B‐splines (NURBS) basis functions. The least‐squares functional is formulated directly in terms of the strong form of the governing equations and boundary conditions. Thus, the introduction of auxiliary variables is avoided, but the order of the basis functions must be higher or equal to the order of the highest spatial derivatives. The methodology is applied to the incompressible Navier–Stokes equations and to linear as well as nonlinear elastic solid mechanics. The numerical examples presented feature convective effects and incompressible or nearly incompressible material. The numerical results, which are obtained with equal‐order interpolation and without any stabilisation techniques, are smooth and accurate. It is shown that for p and h refinement, the theoretical rates of convergence are achieved. Copyright © 2014 John Wiley & Sons, Ltd.