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Mon Dec 12 11:46:10 PST 2011

nsient advection-<br>
diffusion problems, in Comput. Methods Appl. Mech Eng, v. 193, 2004, p 2301=
they point out that:<br>
&quot;Regarding the small localized oscillations in SUPG solutions we recal=
l that SUPG is not monotonicity<br>
preserving, and that such oscillations can be expected in the vicinity of d=
iscontinuities and internal layers.<br>
Therefore, their presence cannot serve as an indication of a destabilizatio=
n. Moreover, as the data in<br>
Tables 1=E2=80=933 show, smaller time steps do not lead to an increase in t=
he H1 seminorm of the solutions,<br>
=C2=A0i.e., these oscillations remain bounded for small time steps. An appl=
ication of a discontinuity capturing<br>
operator [16] is recommended for a further suppression of these oscillation=
s.<br></blockquote></blockquote><div><br></div><div>My opinion is that thes=
e guys are using analysis tools that aren&#39;t really appropriate. It&#39;=
s interesting math, but tends not to acknowledge Godunov&#39;s theorem and,=
 in my opinion, gives much less useful results than the finite volume/DG co=
mmunity (see Chi-Wang Shu&#39;s various review papers for that perspective)=
<div><br></div></div><div>Here is a recent review comparing transport schem=
es. It&#39;s still written from a FEM perspective, but branches out in a go=
od way.</div><br><div><a href=3D"
<div><br></div><div>I&#39;ll also mention that there are some newer exotic =
high-order methods such as &quot;spectral difference&quot; that have some n=
ice properties, but still aren&#39;t very mature.</div><div><br></div>


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