NDLI: Energy Stable and Momentum Conserving Hybrid Finite Element Method for the Incompressible NavierStokes Equations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Wells, Garth N. Labeur, Robert Jan
Copyright Year	2012
Abstract	A hybrid method for the incompressible NavierStokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the NavierStokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations.
Starting Page	A889
Ending Page	A913
Page Count	25
File Format	PDF
ISSN	10648275
DOI	10.1137/100818583
e-ISSN	10957197
Issue Number	2
Volume Number	34
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-03-27
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods finite element method hybrid finite element methods incompressible NavierStokes equations Stokes and related (Oseen, etc.) flows Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Navier-Stokes equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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