fix: sfem example typo errors (#3711)

* fix: implemented changes

* chore: adding changelog file 3711.fixed.md [dependabot-skip]

---------

Co-authored-by: pyansys-ci-bot <[email protected]>

Author: moe-ad

doc/changelog.d/3711.fixed.md

@@ -0,0 +1 @@
+fix: sfem example typo errors

doc/source/examples/extended_examples/sfem/sfem.py

@@ -399,8 +399,8 @@ def young_modulus_realization(
 # Plot of ensemble variance
 fig, ax = plt.subplots()
 fig.set_size_inches(15, 8)
-ax.plot(ensemble_var_with_realization, label="Actual variance")
-ax.axhline(y=1e8, color="r", linestyle="dashed", label="Computed variance")
+ax.plot(ensemble_var_with_realization, label="Computed variance")
+ax.axhline(y=1e8, color="r", linestyle="dashed", label="Actual variance")
 plt.xlabel("No of realizations")
 plt.ylabel(r"Ensemble varianc of $E$")
 ax.grid(True)

doc/source/examples/extended_examples/sfem/stochastic_fem.rst

@@ -204,7 +204,7 @@ distribution and for each of these samples solving the deterministic problem:
 
 .. math:: \pmb{K}(\pmb{\xi}_{(i)})\pmb{U}(\pmb{\xi}_{(i)}) = \pmb{F}(\pmb{\xi}_{(i)})
 
-The next step is to collect the :math:`N_{sim}` response vectors :math:`\pmb{U} := \pmb{U}(\pmb{\xi}_{(i)})` and perform a statistical
+The next step is to collect the :math:`N_{sim}` response vectors :math:`\pmb{U_i} := \pmb{U}(\pmb{\xi}_{(i)})` and perform a statistical
 postprocessing to extract useful information such as mean value, variance, histogram, and
 empirical PDF.
 
@@ -217,7 +217,7 @@ The following plane stress problem shows a two-dimensional cantilever structure
 
    A two-dimensional cantilever structure under a point load.
 
-:math:`P` is a random variable following the Gaussian distribution :math:`\mathcal{N}(0,1)` (kN), and the modulus of elasticity is a
+:math:`P` is a random variable following the Gaussian distribution :math:`\mathcal{N}(10,2)` (kN), and the modulus of elasticity is a
 random field given by this expression:
 
 .. math:: E(x) = 10^5(1+0.10f(x)) (kN/m^2)
@@ -364,7 +364,7 @@ This function implements the preceding steps:
 
 .. literalinclude:: sfem.py
   :language: python
-  :lines: 444-556
+  :lines: 414-556
 
 You can pass the required arguments to the defined function to run the simulations: