From: Wolfgang Bangerth Date: Tue, 14 Jan 2020 00:28:17 +0000 (-0700) Subject: Add a few links to step-6. X-Git-Tag: v9.2.0-rc1~687^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F9311%2Fhead;p=dealii.git Add a few links to step-6. --- diff --git a/examples/step-6/doc/results.dox b/examples/step-6/doc/results.dox index 229f662a62..5ccda26cdb 100644 --- a/examples/step-6/doc/results.dox +++ b/examples/step-6/doc/results.dox @@ -493,10 +493,16 @@ solution. In general, if the coefficient $a(\mathbf x)$ is discontinuous along a line in 2d, or a plane in 3d, then the solution may have a kink, but the gradient of the solution will not go to infinity. That means, that the solution is at least -still in the space $W^{1,\infty}$. On the other hand, we know that in the most +still in the Sobolev space +$W^{1,\infty}$ (i.e., roughly speaking, in the +space of functions whose derivatives are bounded). On the other hand, +we know that in the most extreme cases -- i.e., where the domain has reentrant corners, the right hand side only satisfies $f\in H^{-1}$, or the coefficient $a$ is only in -$L^\infty$ -- all we can expect is that $u\in H^1$, a much larger space than +$L^\infty$ -- all we can expect is that $u\in H^1$ (i.e., the +Sobolev +space of functions whose derivative is square integrable), a much larger space than $W^{1,\infty}$. It is not very difficult to create cases where the solution is in a space $H^{1+s}$ where we can get $s$ to become as small as we want. Such cases are often used to test adaptive finite element