From 23538f850f03432ab0174673b07df9038d7e6005 Mon Sep 17 00:00:00 2001 From: David Wells Date: Wed, 12 Oct 2016 11:56:51 -0400 Subject: [PATCH] Improve the step-11 quadrature order explanation. This little commit fixes three little issues with this paragraph: 1. A Gauss quadrature rule has order 2 r - 1 for r points, not 2 r + 1 2. p and p + 1 should be surrounded by $s 3. @>= should be replaced by the TeX command \geq --- examples/step-11/step-11.cc | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/examples/step-11/step-11.cc b/examples/step-11/step-11.cc index 7ef0f3a1df..4f0d19abf3 100644 --- a/examples/step-11/step-11.cc +++ b/examples/step-11/step-11.cc @@ -298,11 +298,11 @@ namespace Step11 // integrate over bilinear shape functions, so we know that we have to use // at least an order two Gauss quadrature formula. On the other hand, we // want the quadrature rule to have at least the order of the boundary - // approximation. Since the order of Gauss rule with $r$ points is $2r + + // approximation. Since the order of Gauss rule with $r$ points is $2r - // 1$, and the order of the boundary approximation using polynomials of - // degree p is p+1, we know that $2r@>=p$. Since r has to be an integer - // and (as mentioned above) has to be at least 2, this makes up for the - // formula above computing gauss_degree. + // degree $p$ is $p+1$, we know that $2r \geq p$. Since r has to be an + // integer and (as mentioned above) has to be at least $2$, this makes up + // for the formula above computing gauss_degree. // // Since the generation of the body force contributions to the right hand // side vector was so simple, we do that all over again for the boundary -- 2.39.5