Conservation properties for the Galerkin and stabilised forms of the advection–diffusion and incompressible Navier–Stokes equations

Thomas J.R. Hughes, Garth N. Wells
2005 Computer Methods in Applied Mechanics and Engineering  
A common criticism of continuous Galerkin finite element methods is their perceived lack of conservation. This may in fact be true for incompressible flows when advective, rather than conservative, weak forms are employed. However, advective forms are often preferred on grounds of accuracy despite violation of conservation. It is shown here that this deficiency can be easily remedied, and conservative procedures for advective forms can be developed from multiscale concepts. As a result,
more » ... tive stabilised finite element procedures are presented for the advection-diffusion and incompressible Navier-Stokes equations. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.
doi:10.1016/j.cma.2004.06.034 fatcat:rtxeoghvoffjnfrpkzrbcsb2rm