From: Wolfgang Bangerth Date: Sat, 18 May 2019 10:45:56 +0000 (-0600) Subject: Mention step-61 in the introduction of step-51. X-Git-Tag: v9.1.0-rc3~6^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=8f9ff8a121c8b57028dcad467a0fc2809b34cef9;p=dealii.git Mention step-61 in the introduction of step-51. --- diff --git a/examples/step-51/doc/builds-on b/examples/step-51/doc/builds-on index f1818ebf1b..da87e7fb0a 100644 --- a/examples/step-51/doc/builds-on +++ b/examples/step-51/doc/builds-on @@ -1 +1 @@ -step-7 step-9 +step-7 step-9 step-61 diff --git a/examples/step-51/doc/intro.dox b/examples/step-51/doc/intro.dox index 1ab7b75c79..fb63724b66 100644 --- a/examples/step-51/doc/intro.dox +++ b/examples/step-51/doc/intro.dox @@ -41,7 +41,7 @@ this goal by formulating the mathematical problem using Dirichlet-to-Neumann mappings. The partial differential equations are first written as a first order system, and each field is then discretized via a DG method. At this point, the single-valued "trace" values on the skeleton of the -mesh, i.e. element faces, are taken to be independent unknown quantities. +mesh, i.e., element faces, are taken to be independent unknown quantities. This yields unknowns in the discrete formulation that fall into two categories: - Face unknowns that only couple with the cell unknowns from both sides of the face; - Cell unknowns that only couple with the cell and face unknowns @@ -101,6 +101,13 @@ super-convergence property can be used to post-process a new approximate solution that converges at the rate $\mathcal{O}(h^{p+2})$. +

Alternative approaches

+ +The hybridizable discontinuous Galerkin method is only one way in +which the problems of the discontinuous Galerkin method can be +addressed. Another idea is what is called the "weak Galerkin" +method. It is explored in step-61. +

HDG applied to the convection-diffusion problem