<div dir="ltr"><div class="gmail_quote"><div dir="ltr">On Mon, Oct 1, 2018 at 6:31 PM Weizhuo Wang <<a href="mailto:weizhuo2@illinois.edu">weizhuo2@illinois.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Hi!<div><br></div><div>I'm recently trying out the example code provided with the KSP solver (ex12.c). I noticed that the mean norm of the grid increases as I use finer meshes. For example, the mean norm is 5.72e-8 at m=10 n=10. However at m=100, n=100, mean norm increases to 9.55e-6. This seems counter intuitive, since most of the time error should decreases when using finer grid. Am I doing this wrong?</div></div></blockquote><div><br></div><div>The norm is misleading in that it is the l_2 norm, meaning just the sqrt of the sum of the squares of</div><div>the vector entries. It should be scaled by the volume element to approximate a scale-independent</div><div>norm (like the L_2 norm).</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>Thanks! <br>-- <br><div dir="ltr" class="m_2412266254323119974gmail_signature" data-smartmail="gmail_signature"><div dir="ltr">Wang Weizhuo</div></div></div></div>
</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>