From 093119116aba4a7a251652d37c7836b437d6400a Mon Sep 17 00:00:00 2001 From: David Wells Date: Fri, 29 Jun 2018 09:17:41 -0400 Subject: [PATCH] Delete some trailing whitespace. --- examples/step-11/doc/intro.dox | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/examples/step-11/doc/intro.dox b/examples/step-11/doc/intro.dox index ed8619296f..a3048cba28 100644 --- a/examples/step-11/doc/intro.dox +++ b/examples/step-11/doc/intro.dox @@ -21,7 +21,7 @@ The compatibility condition allows a solution of the above equation, but it nevertheless retains an ambiguity: since only derivatives of the solution appear in the equations, the solution is only determined up to a constant. For this reason, we have to pose another condition for the numerical solution, -which fixes this constant. +which fixes this constant. For this, there are various possibilities:
    @@ -33,13 +33,13 @@ For this, there are various possibilities: functions. Therefore, even though fixing one node is allowed for discretized functions, it is not for continuous functions, and one can often see this in a resulting error spike at this point in the numerical - solution. - + solution. +
  1. Fixing the mean value over the domain to zero or any other value. This is allowed on the continuous level, since $H^1(\Omega)\subset L^1(\Omega)$ by Sobolev's inequality, and thus also on the discrete level since we there only consider subsets of $H^1$. - +
  2. Fixing the mean value over the boundary of the domain to zero or any other value. This is also allowed on the continuous level, since $H^{1/2}(\partial\Omega)\subset L^1(\partial\Omega)$, again by Sobolev's -- 2.39.5