Abstract
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, conservative stabilised finite element procedures are
presented for the advection-diffusion and incompressible Navier-Stokes
equations.
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