diff --git a/chapter3/robin_neumann_dirichlet.ipynb b/chapter3/robin_neumann_dirichlet.ipynb index ce17f02c..e11c6e4d 100644 --- a/chapter3/robin_neumann_dirichlet.ipynb +++ b/chapter3/robin_neumann_dirichlet.ipynb @@ -49,7 +49,7 @@ "On the Dirichlet part ($\\Gamma_D^i$), the boundary integral vanishes since $v=0$. On the remaining part of the boundary, we split the boundary into contributions from the Neumann parts ($\\Gamma_N^i$) and Robin parts ($\\Gamma_R^i$). Inserting the boundary conditions, we obtain\n", "\n", "$$\n", - "-\\int_{\\Omega}\\kappa\\frac{\\partial u }{\\partial n }v~\\mathrm{d} s=\\sum_i \\int_{\\Gamma_N^i} g_i~\\mathrm{d} s + \\sum_i\\int_{\\Gamma_R^i}r_i(u-s_i)~\\mathrm{d}s.\n", + "-\\int_{\\partial\\Omega}\\kappa\\frac{\\partial u }{\\partial n }v~\\mathrm{d} s=\\sum_i \\int_{\\Gamma_N^i} g_i~\\mathrm{d} s + \\sum_i\\int_{\\Gamma_R^i}r_i(u-s_i)~\\mathrm{d}s.\n", "$$\n", "\n", "Thus we have the following variational problem\n",