From: Wolfgang Bangerth Date: Sun, 6 May 2018 13:20:34 +0000 (-0600) Subject: Add a reference to step-10. X-Git-Tag: v9.1.0-rc1~1203^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F6495%2Fhead;p=dealii.git Add a reference to step-10. While there, also rewrite a couple of sentences. --- diff --git a/examples/step-10/doc/results.dox b/examples/step-10/doc/results.dox index 208f274573..4b37071c78 100644 --- a/examples/step-10/doc/results.dox +++ b/examples/step-10/doc/results.dox @@ -19,7 +19,10 @@ the aspect ratio of the generated output is actually 1:1, i.e. a circle is drawn as a circle on your screen, rather than as an ellipse. The third line switches off the key in the graphic, as that will only print information (the filename) which is not that important -right now. Similarly, the third and fourth disable tic marks. +right now. Similarly, the third and fourth disable tic marks. The plot +is then generated with a specific line width ("`lw`", here set to 4) +and line type ("`lt`", here chosen by saying that the line should be +drawn using the RGB color "black"). The following table shows the triangulated computational domain for $Q_1$, $Q_2$, and $Q_3$ mappings, for the original coarse grid (left), and a once @@ -209,5 +212,8 @@ that are based on the p+1 point Gauss-Lobatto quadrature rule that selects the support points in such a way that the quadrature rule converges at order 2p. Even though these points are here only used for interpolation of a pth order polynomial, we get a superconvergence effect when -numerically evaluating the integral that actually gives this high order of -convergence. +numerically evaluating the integral, resulting in the observed high order of +convergence. (This effect is also discussed in detail in the following +publication: A. Bonito, A. Demlow, and J. Owen: "A priori error +estimates for finite element approximations to eigenvalues and +eigenfunctions of the Laplace-Beltrami operator", submitted, 2018.)