No subject

nsient advection-<br>
diffusion problems, in Comput. Methods Appl. Mech Eng, v. 193, 2004, p 2301=
-2323),<br>
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=963 show, smaller time steps do not lead to an increase in the H1 =
seminorm of the solutions,<br>
=A0i.e., these oscillations remain bounded for small time steps. An applica=
tion of a discontinuity capturing<br>
operator [16] is recommended for a further suppression of these oscillation=
s.<br></blockquote></blockquote><div><br></div></div><div>My opinion is tha=
t these guys are using analysis tools that aren&#39;t really appropriate. I=
t&#39;s interesting math, but tends not to acknowledge Godunov&#39;s theore=
m and, in my opinion, gives much less useful results than the finite volume=
/DG community (see Chi-Wang Shu&#39;s various review papers for that perspe=
ctive).</div>

<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"http://www.wias-berlin.de/people/john/ELEC=
TRONIC_PAPERS/JN12.JCP.pdf" target=3D"_blank">http://www.wias-berlin.de/peo=
ple/john/ELECTRONIC_PAPERS/JN12.JCP.pdf</a></div>

<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>

</blockquote></div><br><br clear=3D"all"><div><br></div>-- <br>What most ex=
perimenters take for granted before they begin their experiments is infinit=
ely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener<br>

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