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

Kadapa, C.; Dettmer, W.G.; Peri?, D.


W.G. Dettmer

D. Peri?


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.

Journal Article Type Article
Acceptance Date Jul 18, 2014
Online Publication Date Mar 2, 2015
Publication Date Feb 17, 2015
Deposit Date Aug 29, 2022
Journal International Journal for Numerical Methods in Engineering
Print ISSN 0029-5981
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 101
Issue 7
Pages 521-539
Keywords FEM, NURBS, isogeometric analysis, least-squares, Navier–Stokes, elasticity, incompressibility
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