Nodal basis for Maxwell's equations

Question

Hi,

I'm looking to create the function space
$$
\textbf{H}^1_{\tau}(\Omega) = \{ \overrightarrow{v} \in (\textbf{H}^1(\Omega))^d: \overrightarrow{v} \times \overrightarrow{n} = 0 \},
$$
where $\overrightarrow{n}$ is the normal to the domain $\Omega$. Is this possible?

Answer 1

Use zero Dirichlet condition on some H(curl) space, see chapter 3.5 in FEniCS book.

Comments

If I use a H(curl) space (as in chapter 3.5 of the FEniCS book) then I will be using Nedelec elements which are edge elements. I'm looking to discretise Maxwell's equations using nodal elements, is this possible in FEniCS?

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Ok, I was wrong. As long as your boundaries are aligned with axis you can achieve this with component-wise DirichletBC and Lagrange element.

But I'm afraid that with Lagrange elements you cannot achieve this in principle with general boundary. The Nitsche method is often use to circumvent this.