examples/navier-stokes.md

@@ -21,7 +21,7 @@ The pair $`\big(\mathbf{u}(t,\cdot), p(t,\cdot)\big)`$ is thus in the product sp
 
 A linearized time-discretization with a semi-implicit backward Euler scheme then reads: for $`k=0,1,2,\ldots N`$ find $`\mathbf{u}^{k+1}\in\mathbf{V}_\mathbf{g}, p\in Q`$, s.t.
 ```math
-\int_\Omega \varrho\big(\frac{1}{\tau}(\mathbf{u}^{k+1} - \mathbf{u}^k) + (\mathbf{u}^k\cdot\nabla)\mathbf{u}^{k+1}\big)\cdot\mathbf{v} + \nu\nabla\mathbf{u}^{k+1}:\nabla\mathbf{v} + p\,\nabla\cdot\mathbf{v}\,\text{d}\mathbf{x} = \int_\Omega \mathbf{f}(t^{k+1})\cdot\mathbf{v}\,\text{d}\mathbf{x},\qquad\forall \mathbf{v}\in \mathbf{V}_0, \\
+\int_\Omega \varrho\Big(\frac{1}{\tau}(\mathbf{u}^{k+1} - \mathbf{u}^k) + (\mathbf{u}^k\cdot\nabla)\mathbf{u}^{k+1}\Big)\cdot\mathbf{v} + \nu\nabla\mathbf{u}^{k+1}:\nabla\mathbf{v} + p\,\nabla\cdot\mathbf{v}\,\text{d}\mathbf{x} = \int_\Omega \mathbf{f}(t^{k+1})\cdot\mathbf{v}\,\text{d}\mathbf{x},\qquad\forall \mathbf{v}\in \mathbf{V}_0, \\
 \int_\Omega q\,\nabla\cdot\mathbf{u}^{k+1}\,\text{d}\mathbf{x} = 0,\qquad \forall q\in Q.
 ```
-with $`0=t^0<t^1<\ldots < t^k <\ldots<t^N=T`$, $`\tau=t^{k+1} - t^k`$, and given $`\mathbf{u}^0`$.
+with $`0=t^0<t^1<\ldots<t^N=T`$, timestep $`\tau=t^{k+1} - t^k`$, and given initial velocity $`\mathbf{u}^0`$.