From 80161c5216de1d492854fd77245d56253058712c Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Thu, 6 Apr 2017 08:34:08 -0600 Subject: [PATCH] Minor updates to the documentation of FE_Q_iso_Q1. --- include/deal.II/fe/fe_q_iso_q1.h | 16 ++++++++++------ 1 file changed, 10 insertions(+), 6 deletions(-) diff --git a/include/deal.II/fe/fe_q_iso_q1.h b/include/deal.II/fe/fe_q_iso_q1.h index d163801c97..cd065cd351 100644 --- a/include/deal.II/fe/fe_q_iso_q1.h +++ b/include/deal.II/fe/fe_q_iso_q1.h @@ -1,6 +1,6 @@ // --------------------------------------------------------------------- // -// Copyright (C) 2000 - 2016 by the deal.II authors +// Copyright (C) 2000 - 2017 by the deal.II authors // // This file is part of the deal.II library. // @@ -34,7 +34,8 @@ DEAL_II_NAMESPACE_OPEN * with the same number of degrees of freedom as the @p Qp elements but using * linear interpolation instead of higher order one. This type of element is * also called macro element in the literature as it really consists of - * several smaller elements, namely pdim. + * several smaller elements, namely pdim such + * sub-cells. * * The numbering of degrees of freedom is done in exactly the same way as in * FE_Q of degree @p p. See there for a detailed description on how degrees of @@ -52,24 +53,27 @@ DEAL_II_NAMESPACE_OPEN * whereas these elements reach only (h/p)2. For these two * reasons, this element is usually not very useful as a standalone. In * addition, any evaluation of face terms on the boundaries within the - * elements becomes impossible with this element. + * elements becomes impossible with this element because deal.II does not + * have the equivalent of FEFaceValues for lower-dimensional integrals + * in the interior of cells. * * Nonetheless, there are a few use cases where this element actually is * useful: *
    * *
  1. Systems of PDEs where certain variables demand for higher resolutions - * than the others and the additional degrees of freedom should be spend on + * than the others and the additional degrees of freedom should be spent on * increasing the resolution of linears instead of higher order polynomials, * and you do not want to use two different meshes for the different * components. This can be the case when irregularities (shocks) appear in the * solution and stabilization techniques are used that work for linears but * not higher order elements.
  2. * - *
  3. Stokes/Navier Stokes systems as the one discussed in step-22 could be + *
  4. Stokes/Navier Stokes systems such as the one discussed in step-22 could be * solved with Q2-iso-Q1 elements for velocities instead of Q2 elements. * Combined with Q1 pressures they give a stable mixed element pair. However, - * they perform worse than the standard approach in most situations.
  5. + * they perform worse than the standard (Taylor-Hood $Q_2\times Q_1$) + * approach in most situations. * *
  6. Preconditioning systems of FE_Q systems of higher order @p p with a * preconditioner based on @p Qp-iso-Q1 elements: Some preconditioners like -- 2.39.5