diff --git a/chapter2/navierstokes.md b/chapter2/navierstokes.md index 336562cc..938115c3 100644 --- a/chapter2/navierstokes.md +++ b/chapter2/navierstokes.md @@ -68,11 +68,11 @@ As mentioned in the note in [Linear elasticity implementation](./linearelasticit $w_i=\sum_{j}\left(u_j\frac{\partial}{\partial x_j}\right)u_i = \sum_j u_j\frac{\partial u_i}{\partial x_j}$. This term can be implemented in FEniCSx as either `grad(u)*u`, since this expression becomes $\sum_j\frac{\partial u_i}{\partial x_j}u_j$, or as `dot(u, nabla_grad(u))` since this -expression becomes $\sum_i u_i\frac{\partial u_j}{x_i}$. We will use the notation `dot(u, nabla_grad(u))` below since it corresponds more closely to the standard notation $u\cdot \nabla u$. +expression becomes $\sum_i u_i\frac{\partial u_j}{\partial x_i}$. We will use the notation `dot(u, nabla_grad(u))` below since it corresponds more closely to the standard notation $u\cdot \nabla u$. ``` We now move on to the second step in our splitting scheme for the incompressible Navier-Stokes equations. In the first step, we computed the *tentative velocity* $u^*$ based on the pressure from the previous time step. -We may now use the computed tentative velocity to compute the new pressure $p^n$: +We may now use the computed tentative velocity to compute the new pressure $p^{n+1}$: ```{math} :label: ipcs-two \langle \nabla p^{n+1}, \nabla q \rangle = \langle \nabla p^n, \nabla q\rangle - \frac{\rho}{\Delta t}\langle \nabla \cdot u^*, q\rangle. diff --git a/pyproject.toml b/pyproject.toml index 399e85f4..ee1104ec 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -6,7 +6,7 @@ build-backend = "setuptools.build_meta" name = "DOLFINx_Tutorial" version = "0.10.0" dependencies = [ - "jupyter-book", + "jupyter-book<2.0", "meshio", "h5py", "seaborn",