@@ -17,4 +17,4 @@ In a weak variational formulation, we try to find $`\mathbf{u}(t,\cdot)\in \math
...
@@ -17,4 +17,4 @@ In a weak variational formulation, we try to find $`\mathbf{u}(t,\cdot)\in \math
```
```
for $`t\in[0,T]`$.
for $`t\in[0,T]`$.
The pair $`\big(\mathbf{u}(t,\cdot), p(t,\cdot)\big)`$ is thus in the product space $`\mathbf{V}_\mathbf{g}\times L^2(\Omega)`$ where $`\mathbf{V}_\mathbf{g}`$ is also a product space of $`H^1`$ spaces, i.e., $`\mathbf{V}_\mathbf{g}=V_{g_0}\times V_{g_1}\times V_{g_2}\simeq [V_{g_i}]^d`$. Later, this space will be approximated with a Taylor-Hood space of piecewise quadratic and linear functions.
The pair $`\big(\mathbf{u}(t,\cdot), p(t,\cdot)\big)`$ is thus in the product space $`\mathbf{V}_\mathbf{g}\times Q`$ where $`\mathbf{V}_\mathbf{g}`$ is also a product of $`H^1`$ spaces, i.e., $`\mathbf{V}_\mathbf{g}=V_{g_0}\times V_{g_1}\times V_{g_2}\simeq [V_{g_i}]^d`$. Later, this space will be approximated with a Taylor-Hood space of piecewise quadratic and linear functions.