Add propsoed solution to #205 (#257)

Author: jorgensd

chapter3/component_bc.ipynb

@@ -118,7 +118,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Next, we locate the degrees of freedom on the top boundary. However, as the boundary condition is in a sub space of our solution, we need to supply both the parent space $V$ and the sub space $V_0$ to `dolfinx.locate_dofs_topological`."
+    "Next, we locate the degrees of freedom on the top boundary.\n",
+    "However, as the boundary condition is in a sub space of our solution,\n",
+    "we have to carefully decide whoe to locate the degrees of freedom.\n",
+    "In the example below, we will use a constant value as the prescribed value.\n",
+    "This means that we can use `dolfinx.fem.locate_dofs_topological`\n",
+    "on the (un-collapsed) sub space to locate the degrees of freedom on the boundary.\n",
+    "If you want to use a spatially dependent function, see\n",
+    "[FEniCS Workshop: Dirichlet conditions in mixed spaces](https://jsdokken.com/FEniCS-workshop/src/deep_dive/mixed_problems.html#dirichlet-conditions-in-mixed-spaces)\n",
+    "for a detailed discussion."
    ]
   },
   {
@@ -285,7 +293,7 @@
     "if not pyvista.OFF_SCREEN:\n",
     "    p.show()\n",
     "else:\n",
-    "    fig_array = p.screenshot(f\"component.png\")"
+    "    fig_array = p.screenshot(\"component.png\")"
    ]
   }
  ],

chapter3/component_bc.py

@@ -87,7 +87,15 @@ def clamped_boundary(x):
 # Next we would like to constrain the $x$-component of our solution at $x=L$ to $0$. We start by creating the sub space only containing the $x$
 # -component.
 
-# Next, we locate the degrees of freedom on the top boundary. However, as the boundary condition is in a sub space of our solution, we need to supply both the parent space $V$ and the sub space $V_0$ to `dolfinx.locate_dofs_topological`.
+# Next, we locate the degrees of freedom on the top boundary.
+# However, as the boundary condition is in a sub space of our solution,
+# we have to carefully decide whoe to locate the degrees of freedom.
+# In the example below, we will use a constant value as the prescribed value.
+# This means that we can use `dolfinx.fem.locate_dofs_topological`
+# on the (un-collapsed) sub space to locate the degrees of freedom on the boundary.
+# If you want to use a spatially dependent function, see
+# [FEniCS Workshop: Dirichlet conditions in mixed spaces](https://jsdokken.com/FEniCS-workshop/src/deep_dive/mixed_problems.html#dirichlet-conditions-in-mixed-spaces)
+# for a detailed discussion.
 
 def right(x):
     return np.logical_and(np.isclose(x[0], L), x[1] < H)
@@ -157,4 +165,4 @@ def sigma(u):
 if not pyvista.OFF_SCREEN:
     p.show()
 else:
-    fig_array = p.screenshot(f"component.png")
+    fig_array = p.screenshot("component.png")