diff --git a/lessons/15_Step_12.ipynb b/lessons/15_Step_12.ipynb
index 30d1a927..9c957653 100644
--- a/lessons/15_Step_12.ipynb
+++ b/lessons/15_Step_12.ipynb
@@ -221,7 +221,7 @@
    "outputs": [],
    "source": [
     "def pressure_poisson_periodic(p, dx, dy):\n",
-    "    pn = numpy.empty_like(p)\n",
+    "    pn[:] = numpy.empty_like(p)\n",
     "    \n",
     "    for q in range(nit):\n",
     "        pn = p.copy()\n",
@@ -313,10 +313,10 @@
     "stepcount = 0\n",
     "\n",
     "while udiff > .001:\n",
-    "    un = u.copy()\n",
-    "    vn = v.copy()\n",
+    "    un[:] = u.copy()\n",
+    "    vn[:] = v.copy()\n",
     "\n",
-    "    b = build_up_b(rho, dt, dx, dy, u, v)\n",
+    "    b[:] = build_up_b(rho, dt, dx, dy, u, v)\n",
     "    p = pressure_poisson_periodic(p, dx, dy)\n",
     "\n",
     "    u[1:-1, 1:-1] = (un[1:-1, 1:-1] -\n",