Update nitsche.ipynb (#37)

* Update nitsche.ipynb

corrected the weak form

* Apply suggestions from code review

Consistent usage of $n \cdot \nabla .. $

Co-authored-by: Jørgen Schartum Dokken <[email protected]>

Author: arashgmn

chapter1/nitsche.ipynb

@@ -74,8 +74,8 @@
     "$u_D$ is the known Dirichlet condition, and $h$ is the circumradius of the mesh element.\n",
     "We create bilinear and linear form, $a$ and $L$\n",
     "\\begin{align}\n",
-    "    a(u, v) &= \\int_{\\Omega} \\nabla u \\cdot \\nabla v~\\mathrm{d}x + \\int_{\\partial\\Omega}-(n \\cdot\\nabla u) v - (n \\cdot \\nabla v) u - \\frac{\\alpha}{h} uv~\\mathrm{d}s,\\\\\n",
-    "    L(v) &= \\int_{\\Omega} fv~\\mathrm{d}x + \\int_{\\partial\\Omega}  -(\\nabla u_D \\cdot n) v  -(\\nabla v \\cdot n) u_D + \\frac{\\alpha}{h} u_Dv~\\mathrm{d}s\n",
+    "    a(u, v) &= \\int_{\\Omega} \\nabla u \\cdot \\nabla v~\\mathrm{d}x + \\int_{\\partial\\Omega}-(n \\cdot\\nabla u) v - (n \\cdot \\nabla v) u + \\frac{\\alpha}{h} uv~\\mathrm{d}s,\\\\\n",
+    "    L(v) &= \\int_{\\Omega} fv~\\mathrm{d}x + \\int_{\\partial\\Omega} -(n \\cdot \\nabla) u_D + \\frac{\\alpha}{h} u_Dv~\\mathrm{d}s\n",
     "\\end{align}"
    ]
   },
@@ -274,4 +274,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}