From fabb4f931403e945802fc2360926239fea0c0ad7 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Tue, 23 Apr 2019 18:30:37 -0600 Subject: [PATCH] Break long lines in step-61/doc/results.dox. --- examples/step-61/doc/results.dox | 37 +++++++++++++++++++++++++------- 1 file changed, 29 insertions(+), 8 deletions(-) diff --git a/examples/step-61/doc/results.dox b/examples/step-61/doc/results.dox index 6b7efd1aab..37eb72eccf 100644 --- a/examples/step-61/doc/results.dox +++ b/examples/step-61/doc/results.dox @@ -1,9 +1,20 @@

Results

-We run the test example $p = \sin(\pi x) \sin(\pi y)$ with homogenous Dirichelet boundary conditions in the domain $\Omega = (0,1)^2$. And $\mathbf{K}$ is the identity matrix. We test it on $\mbox{WG}(Q_0,Q_0;RT_{[0]})$, $\mbox{WG}(Q_1,Q_1;RT_{[1]})$ and $\mbox{WG}(Q_2,Q_2;RT_{[2]})$. We will visualize pressure values in interiors and on faces. We want to see the pressure maximum is around 1 and the minimum is around 0. With the mesh refinement, the convergence rates of pressure, velocity and flux should be around 1 on $\mbox{WG}(Q_0,Q_0;RT_{[0]})$ , 2 on $\mbox{WG}(Q_1,Q_1;RT_{[1]})$, and 3 on $\mbox{WG}(Q_2,Q_2;RT_{[2]})$. +We run the test example $p = \sin(\pi x) \sin(\pi y)$ with homogenous Dirichelet +boundary conditions in the domain $\Omega = (0,1)^2$. And $\mathbf{K}$ is the +identity matrix. We test it on $\mbox{WG}(Q_0,Q_0;RT_{[0]})$, $\mbox{WG}(Q_1,Q_1;RT_{[1]})$ +and $\mbox{WG}(Q_2,Q_2;RT_{[2]})$. We will visualize pressure values in interiors +and on faces. We want to see the pressure maximum is around 1 and the minimum +is around 0. With the mesh refinement, the convergence rates of pressure, +velocity and flux should be around 1 on $\mbox{WG}(Q_0,Q_0;RT_{[0]})$ , 2 on +$\mbox{WG}(Q_1,Q_1;RT_{[1]})$, and 3 on $\mbox{WG}(Q_2,Q_2;RT_{[2]})$. +

Test results on WG(Q0,Q0;RT[0])

-The following figures are interior pressures and face pressures implemented on $\mbox{WG}(Q_0,Q_0;RT_{[0]})$. The mesh is refined 2 times and 4 times separately. + +The following figures are interior pressures and face pressures implemented +on $\mbox{WG}(Q_0,Q_0;RT_{[0]})$. The mesh is refined 2 times and 4 times +separately. @@ -16,8 +27,11 @@ The following figures are interior pressures and face pressures implemented on $
-From the figures, we can see that with the mesh refinement, the maximum and minimum are approaching to what we expect. -Since the mesh is a rectangular mesh and numbers of refinement are even, we have symmetric solutions. From the 3d figures, we can see that on $\mbox{WG}(Q_0,Q_0;RT_{[0]})$, pressure is a constant in the interior of the cell. +From the figures, we can see that with the mesh refinement, the maximum and +minimum are approaching to what we expect. +Since the mesh is a rectangular mesh and numbers of refinement are even, we +have symmetric solutions. From the 3d figures, we can see that on $\mbox{WG}(Q_0,Q_0;RT_{[0]})$, +pressure is a constant in the interior of the cell.

Convergence table

@@ -50,8 +64,13 @@ We can see that the convergence rates of $\mbox{WG}(Q_0,Q_0;RT_{[0]})$ are aroun

Test results on WG(Q1,Q1;RT[1])

-The following figures are interior pressures and face pressures implemented on $\mbox{WG}(Q_1,Q_1;RT_{[1]})$. The mesh is refined 4 times. Compared to the previous figures on -$\mbox{WG}(Q_0,Q_0;RT_{[0]})$, on each cell, the result is not a constant. Because we use higher order polynomials to do approximation. So there are 4 pressure values in one interior, 2 pressure values on each face. We use data_out_face.build_patches (fe.degree) +The following figures are interior pressures and face pressures implemented on +$\mbox{WG}(Q_1,Q_1;RT_{[1]})$. The mesh is refined 4 times. Compared to the +previous figures on +$\mbox{WG}(Q_0,Q_0;RT_{[0]})$, on each cell, the result is not a constant. +Because we use higher order polynomials to do approximation. So there are 4 +pressure values in one interior, 2 pressure values on each face. We use +data_out_face.build_patches (fe.degree) to divide each cell interior into 4 subcells. @@ -89,7 +108,8 @@ The convergence rates of $WG(Q_1,Q_1;RT_{[1]})$ are around 2.

Test results on WG(Q2,Q2;RT[2])

-These are interior pressures and face pressures implemented on $WG(Q_2,Q_2;RT_{[2]})$, with mesh size $h = 1/32$. +These are interior pressures and face pressures implemented on +$WG(Q_2,Q_2;RT_{[2]})$, with mesh size $h = 1/32$.
@@ -100,7 +120,8 @@ These are interior pressures and face pressures implemented on $WG(Q_2,Q_2;RT_{[

Convergence table

-This is the convergence table of $L_2$ errors of pressure, velocity and flux on $\mbox{WG}(Q_2,Q_2;RT_{[2]})$ +This is the convergence table of $L_2$ errors of pressure, velocity and flux +on $\mbox{WG}(Q_2,Q_2;RT_{[2]})$
-- 2.39.5