2D CurlCurl

Hello everybody,

I still try to use a error estimator as presented by Bürg for an hp-refinement method for a Maxwell problem.
Therefore, I need to compute the term
[tex]
\begin{align*}
\Vert \nabla \times \left( \mu^{-1} \nabla \times u_h\right) - \varepsilon \omega^2 u_h \Vert_{L^2 (K)}^2
\end{align*}
[/tex]
on every cell K. I tried to set a new HCurl gridfunction for the curl of u_h, but since curl(u_h) returns the scalar curl
[tex]
\begin{align*}
\operatorname{curl}(u) = \left( \frac{\partial u_2}{\partial x_1} - \frac{\partial u_1}{\partial x_2} \right)
\end{align*}
[/tex]
this does not work (different dimensions).

Has anybody a suggestion how fix this issue?

Best regards,
Phil

Hi Phil,

you can set the curl, which is a scalar, into a L2 GridFunction. Then, you can use the gradient of this GridFunction to compute the curl going from scalar to vector to compute your norm.

Best,
Michael