From 6d82ea626e8b32e008537566b4828e77d01d6540 Mon Sep 17 00:00:00 2001
From: Robert Habel <Robert.Habel@student.tu-freiberg.de>
Date: Wed, 3 Aug 2022 09:27:58 +0200
Subject: [PATCH] [T] Final version
---
.../Disc with a hole_Convergence Analysis.ipynb | 15 ++++++++++++++-
1 file changed, 14 insertions(+), 1 deletion(-)
diff --git a/Tests/Data/Mechanics/Linear/DiscWithHole/Disc with a hole_Convergence Analysis.ipynb b/Tests/Data/Mechanics/Linear/DiscWithHole/Disc with a hole_Convergence Analysis.ipynb
index fa61befa947..157af5de8f8 100644
--- a/Tests/Data/Mechanics/Linear/DiscWithHole/Disc with a hole_Convergence Analysis.ipynb
+++ b/Tests/Data/Mechanics/Linear/DiscWithHole/Disc with a hole_Convergence Analysis.ipynb
@@ -1308,7 +1308,20 @@
"source": [
"The $\\ell_{2}$ norm or Euclidean norm is the square root of the sum of the squared absolute errors at each point of the mesh. \n",
"\n",
- "The root mean square ($RMS$) is calculated similarly. Here, however, the influence of the number of points is taken into account by dividing by the square root of the number of points."
+ "The root mean square ($RMS$) is calculated similarly. Here, however, the influence of the number of points is taken into account by dividing by the square root of the number of points.\n",
+ "\n",
+ "The $L_{2}$ norm as Integral norm represents a generalization of the $\\ell_{2}$ norm for continuous functions. While the Euclidean norm determines the values for individual mesh nodes, the Integral norm considers the course over the entire mesh. Therefor an advantage of the $L_{2}$ norm is, that big elements are considered with a higher impact than small ones, which produces more homogeneous results. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d5a07337-072f-4539-bf9d-7eaac25cbbe4",
+ "metadata": {},
+ "source": [
+ "The following plots represent the development of the Euclidean and Integral norm and $RMS$ for the refinement of the mesh. How fast the considered element converge is expressed by the gradient of the linear curves in the plot. \n",
+ "First the detailed discussed error norms for the stresses are visualised and in addition to them the norms for the associated displacements to draw conclusions about the quality of convergence. \n",
+ "\n",
+ "A main statement that can be made is that the solution for the displacements converge significantly more rapid than for the stresses. The approach of the displacement values for the meshes with decreasing cell sizes to the finest mesh with refinement index 240 is much better than for the regarded stresses. \n"
]
},
{
--
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