these cells.
By construction, there are now three cases to be considered:
-<ul>
-<li>[(i)] The cell $K$ is active on both meshes, i.e. both the basis
+<ol>
+<li> The cell $K$ is active on both meshes, i.e. both the basis
functions $\varphi_g^i$ as well as $\varphi_{g'}^j$ are defined on $K$.
-<li>[(ii)] The cell $K$ is active on mesh $g$, but not $g'$, i.e. the
+<li> The cell $K$ is active on mesh $g$, but not $g'$, i.e. the
$\varphi_g^i$ are defined on $K$, whereas the $\varphi_{g'}^j$ are defined
on children of $K$.
-<li>[(iii)] The cell $K$ is active on mesh $g'$, but not $g$, with opposite
+<li> The cell $K$ is active on mesh $g'$, but not $g$, with opposite
conclusions than in (ii).
-</ul>
+</ol>
To compute the right hand side above, we then need to have different code for
these three cases, as follows:
\qquad
\qquad
F_i|_{K_c} = B_c^{il} M_{K_c}^{lj} \phi_{g'}^j
- = (B_c M_{K_c})^{il} \phi_{g'}^j,
+ = (B_c M_{K_c})^{ij} \phi_{g'}^j,
@f}
where $M_{K_c}^{lj}=\int_{K_c} f(x) \varphi_{g'}^l(x) \varphi_{g'}^j(x)$ is
the weighted mass matrix on child $c$ of cell $K$.
&=&
\left\{
\sum_{0\le c<2^{\texttt{dim}}}
- \int_{K_c} f(x) \varphi_{g'}^i(x) B_c^{jl} \varphi_{g'}^l(x)
+ \int_{K_c} f(x) \varphi_g^i(x) B_c^{jl} \varphi_{g}^l(x)
\ dx \right\} \phi_{g'}^j.
@f}
In matrix notation, this expression now reads as