Paper Info
Title
Least squares finite element method with high continuity NURBS basis for incompressible Navier-Stokes equations
Abstract
Modern least squares finite element method (LSFEM) has advantage over mixed finite element method for non-self-adjoint problem like Navier-Stokes equations, but has problem to be norm equivalent and mass conservative when using C^0 type basis. In this paper, LSFEM with non-uniform B-splines (NURBS) is proposed for Navier-Stokes equations. High order continuity NURBS is used to construct the finite-dimensional spaces for both velocity and pressure. Variational form is derived from the governing equations with primitive variables and the DOFs due to additional variables are not necessary. There is a novel k-refinement which has spectral convergence of least squares functional. The method also has same advantages as isogeometric analysis like automatic mesh generation and exact geometry representation. Several benchmark problems are solved using the proposed method. The results agree well with the benchmark solutions available in literature. The results also show good performance in mass conservation.
Year
DOI
Venue
2014
10.1016/j.jcp.2013.12.031
J. Comput. Physics
Keywords
Field
DocType
automatic mesh generation,high continuity nurbs basis,mixed finite element method,additional variable,incompressible navier-stokes equation,squares finite element method,non-self-adjoint problem,navier-stokes equation,benchmark problem,mass conservation,benchmark solution,least squares,nurbs,fem
Least squares,Convergence (routing),Mathematical optimization,Mathematical analysis,Isogeometric analysis,Finite element method,Mesh generation,Conservation of mass,Mathematics,Navier–Stokes equations,Mixed finite element method
Journal
Volume
ISSN
Citations 
260,
0021-9991
0
PageRank 
References 
Authors
0.34
13
4
Name
Order
Citations
PageRank
Dexiang Chen101.01
Zi-Li Xu222.76
Shi Liu300.34
Yong-Xin Feng468.27