<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
</head>
<body dir="ltr">
<div id="divtagdefaultwrapper" style="font-size:12pt;color:#000000;font-family:Calibri,Helvetica,sans-serif;" dir="ltr">
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">Typically you will see spatial convergence down to a point where temporal errors dominate, then things will level off.</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">See for example Fig. 4 in </p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><a class="OWAAutoLink" id="LPlnk59010" href="http://www.mcs.anl.gov/~fischer/users.pdf" previewremoved="true">www.mcs.anl.gov/~fischer/users.pdf</a></p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">for Figs. 4 and 5 in "Recent Developments in Spectral Element Simulations of Moving Domain Problems", Fischer, Schmitt, Tomboulides.</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">The benefits of high order in space, despite relatively low order in time, derive from the fact that the costs are multiplicative (number of spatial dofs X number of timesteps), and from the fact that spatial
errors typically dominate most high Reynolds number flow problems because of numerical dispersion and dissipation. Having a high-order method allows you to realize minimal numerical dispersion at a relatively low number of points per wavelength.</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">Paul</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
</div>
<hr style="display:inline-block;width:98%" tabindex="-1">
<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Nek5000-users <nek5000-users-bounces@lists.mcs.anl.gov> on behalf of nek5000-users--- via Nek5000-users <nek5000-users@lists.mcs.anl.gov><br>
<b>Sent:</b> Wednesday, November 14, 2018 8:13:06 PM<br>
<b>To:</b> NEK5000<br>
<b>Subject:</b> [Nek5000-users] Accuracy & errors</font>
<div> </div>
</div>
<style>
<!--
@font-face
{font-family:"Cambria Math"}
@font-face
{font-family:DengXian}
@font-face
{font-family:Calibri}
@font-face
{}
p.x_MsoNormal, li.x_MsoNormal, div.x_MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri",sans-serif}
a:x_link, span.x_MsoHyperlink
{color:blue;
text-decoration:underline}
a:x_visited, span.x_MsoHyperlinkFollowed
{color:#954F72;
text-decoration:underline}
.x_MsoChpDefault
{}
@page WordSection1
{margin:1.0in 1.0in 1.0in 1.0in}
div.x_WordSection1
{}
-->
</style>
<div lang="EN-US" link="blue" vlink="#954F72">
<div class="x_WordSection1">
<p class="x_MsoNormal">Dear Nek users,</p>
<p class="x_MsoNormal"> </p>
<p class="x_MsoNormal">I would like to do a quick test to see the difference in accuracy using two different P-orders, i.e. N = 7, and N = 11. The question I have is about the role of time integration errors. If the code uses 2<sup>nd</sup> or 3<sup>rd</sup>
order of integration in time. That means that at some point the time-integration error will be larger than the spatial error. I wonder what are conditions under which it happens? Because once you are in that regime you will not see any difference between
the various methods.</p>
<p class="x_MsoNormal"> </p>
<p class="x_MsoNormal">Thanks for the help.</p>
<p class="x_MsoNormal"> </p>
</div>
</div>
</body>
</html>