From 1abd1ff70826e4ef2f5396985a5fa6c0345e170f Mon Sep 17 00:00:00 2001 From: hartmann Date: Mon, 3 Sep 2001 16:37:51 +0000 Subject: [PATCH] Fix some refs. git-svn-id: https://svn.dealii.org/trunk@4942 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/doc/reports/mapping_q/index.html | 28 ++++++++++++------------ 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/deal.II/doc/reports/mapping_q/index.html b/deal.II/doc/reports/mapping_q/index.html index a669c655b1..b9de700cd0 100644 --- a/deal.II/doc/reports/mapping_q/index.html +++ b/deal.II/doc/reports/mapping_q/index.html @@ -99,7 +99,7 @@ where $\hat K$ to the element K in real space, see Figure -1. +1.
   @@ -240,7 +240,7 @@ points on the unit cell $\sigma $(1) ensures that each of the unit support points + ALT="$\sigma $">(1) ensures that each of the unit support points $\hat K$ based on a tensor product mesh. In the following we only consider the two-dimensional -case, d=2. For that case, Figure 2 +case, d=2. For that case, Figure 2 shows the distributions of the unit support points 2. Thus the first 4p points are placed +2. Thus the first 4p points are placed on the boundary

-According to (2) these points are mapped to the +According to (2) these points are mapped to the mapping support points pk,

-into the Laplace problem (3) yields the +into the Laplace problem (3) yields the zero boundary value problem,

@@ -627,7 +627,7 @@ Discretisation of this problem

-and recalling definitions (1), (5) and (4) gives +and recalling definitions (1), (5) and (4) gives

@@ -691,7 +691,7 @@ T_{ik}=(\hat\nabla \phi_{4p+i}, \hat\nabla \phi_k)_{\hat K}, \quad i=0,\ldots,(p

-The solutions to problem (7) for l=1,2 are +The solutions to problem (7) for l=1,2 are

@@ -783,7 +783,7 @@ p_8=\tfrac{1}{16}\sum_{k=0}^3p_k+\tfrac{3}{16}\sum_{k=4}^7p_k,

-see also Figure 3, left. +see also Figure 3, left.
  
@@ -800,11 +800,11 @@ Left: Coefficients c8,k for Q2 mappin

-For the case that p=3, Figure 3, right, shows the coefficients c12,k of the linear combination for the inner mapping support point p12. The coefficents for the points p13, p14 and p15 can be obtain by rotation of the coefficients. +For the case that p=3, Figure 3, right, shows the coefficients c12,k of the linear combination for the inner mapping support point p12. The coefficents for the points p13, p14 and p15 can be obtain by rotation of the coefficients.

Implementation in deal.II. The coefficients cjk, see -(9), are represented in the MappingQ +(9), are represented in the MappingQ class by the laplace_on_quad_vector as follows

@@ -832,7 +832,7 @@ Hence for a given degree p the the MappingQ class. This is done by calling the MappingQ::set_laplace_on_quad_vector function that includes the coefficients hardcoded for p=2 and p=3 in d=2dimensions, and a routine for computing the coefficients according to -(9) for all other cases. The mapping support +(9) for all other cases. The mapping support points Mapping class. In MappingQ::add_line_support_points), then by calling MappingQ::apply_laplace_vector the remaining (p-1)2inner mapping supports points are computed, where MappingQ::apply_laplace_vector just performes the linear -combination given in (8). +combination given in (8).
-- 2.39.5