Explicitly bracket \frac

Author: Amund211

tasks/advection_diffusion.py

@@ -117,10 +117,12 @@ def u(x, t):
         ndofs,
         6e0 * np.divide(1, ndofs ** (2 / 3)),
         linestyle="dashed",
-        label=r"$O\left(N_{dof}^{-\frac23}\right)$",
+        label=r"$O\left(N_{dof}^{-\frac{2}{3}}\right)$",
     )
 
-    plt.suptitle(r"Periodic advection diffusion - 2nd order space, $\theta = \frac12$")
+    plt.suptitle(
+        r"Periodic advection diffusion - 2nd order space, $\theta = \frac{1}{2}$"
+    )
     plt.title(
         fr"Refinement with constant $r=\frac{{k}}{{h^2}}={r}$, $c={c}, d={d}, t={T}$"
     )
@@ -236,7 +238,7 @@ def u(x, t):
         ndofs,
         6e0 * np.divide(1, ndofs ** (2 / 3)),
         linestyle="dashed",
-        label=r"$O\left(N_{dof}^{-\frac23}\right)$",
+        label=r"$O\left(N_{dof}^{-\frac{2}{3}}\right)$",
     )
 
     plt.title(f"Error at $t={T}$ (log-log)")
@@ -301,7 +303,7 @@ def u(x, t):
         ndofs,
         1.5e2 * np.divide(1, ndofs ** (4 / 3)),
         linestyle="dashed",
-        label=r"$O\left(N_{dof}^{-\frac43}\right)$",
+        label=r"$O\left(N_{dof}^{-\frac{4}{3}}\right)$",
     )
 
     plt.suptitle("Periodic advection diffusion - 4th order spacial discretization")
@@ -490,7 +492,7 @@ def ux(x, t):
         ndofs,
         1e0 * np.divide(1, ndofs ** (2 / 3)),
         linestyle="dashed",
-        label=r"$O\left(N_{dof}^{-\frac23}\right)$",
+        label=r"$O\left(N_{dof}^{-\frac{2}{3}}\right)$",
     )
 
     plt.suptitle("Aperiodic advection diffusion - Neumann - Neumann")
@@ -551,7 +553,7 @@ def u(x, t):
         ndofs,
         4e0 * np.divide(1, ndofs ** (1 / 2)),
         linestyle="dashed",
-        label=r"$O\left(N_{dof}^{-\frac12}\right)$",
+        label=r"$O\left(N_{dof}^{-\frac{1}{2}}\right)$",
     )
 
     plt.suptitle("Periodic advection diffusion - 1st order spacial discretization")

tasks/fem_poisson.py

@@ -232,7 +232,7 @@ def task_5d_afem_solution():
     "u": lambda x: x ** (2 / 3),
     "a": 0,
     "b": 1,
-    "u_text": r"x^{\frac23}",
+    "u_text": r"x^{\frac{2}{3}}",
 }
 
 

tasks/heat_eqn.py

@@ -354,7 +354,7 @@ def task_2bc():
         ndofs,
         1e0 * np.divide(1, ndofs ** (1 / 2)),
         linestyle="dashed",
-        label=r"$O\left(N_{dof}^{-\frac12}\right)$",
+        label=r"$O\left(N_{dof}^{-\frac{1}{2}}\right)$",
     )
 
     plt.grid()
@@ -388,7 +388,7 @@ def task_2br():
         ndofs,
         1e0 * np.divide(1, ndofs ** (2 / 3)),
         linestyle="dashed",
-        label=r"$O\left(N_{dof}^{-\frac23}\right)$",
+        label=r"$O\left(N_{dof}^{-\frac{2}{3}}\right)$",
     )
 
     plt.grid()

tasks/poisson_1D.py

@@ -332,7 +332,7 @@ def f(x):
     plt.suptitle("Poisson's equation - Adaptive mesh refinement")
     plt.title(
         r"$u\left(x\right) = "
-        r"\exp{-\frac{1}{\epsilon} \left(x - \frac12\right)^2},"
+        r"\exp{-\frac{1}{\epsilon} \left(x - \frac{1}{2}\right)^2},"
         fr"\epsilon = \num{{{eps:.2e}}}$"
     )
     plt.xlabel("Internal nodes $M$")
@@ -401,7 +401,7 @@ def f(x):
     plt.suptitle("Poisson's equation - Adaptive vs uniform mesh refinement")
     plt.title(
         r"$u\left(x\right) = "
-        r"\exp{-\frac{1}{\epsilon} \left(x - \frac12\right)^2},"
+        r"\exp{-\frac{1}{\epsilon} \left(x - \frac{1}{2}\right)^2},"
         fr"\epsilon = \num{{{eps:.2e}}}$"
     )
     plt.xlabel("Internal nodes $M$")