How to solve a system with MixedBilinearForm

[Heinrich-BR]

Hi, I understand this is probably a trivial question, but since I'm a beginner with MFEM I would much appreciate a nudge in the right direction. I'm trying to solve for a vector variable $\mathbf{u}$ in a system with equation $\nabla\cdot \mathbf{u}=0$ plus boundary conditions, with $\mathbf{u}$ in $Hcurl$. Multiplying by $H1$ test functions $v$ and performing the usual integration by parts, we end up with

$(\mathbf{u},\nabla v)=\langle\mathbf{u}\cdot \mathbf{\hat n},v\rangle$.

It seems to me the correct integrator for this would be the MixedVectorWeakDivergenceIntegrator in the domain within a MixedBilinearForm, with some Linear Form boundary integrator on the right-hand side (we assume $\mathbf{u}\cdot \mathbf{\hat n}$ is a known fuction $f$). However, it is my first time trying to solve with rectangular matrices and I'm a bit lost as to what to do after assembling and finalizing the forms. It seems that MixedBilinearForm doesn't have a FormLinearSystem method, so I need to do this manually. Unfortunately, everything I have tried so far has led me into a different MFEM_ABORT, and the examples with Mixed Forms weren't particularly relevant for my specific use case.

So assume I have a MixedBilinearForm(fespace_hcurl,fespace_h1) called a, a LinearForm(fespace_h1) called b, and a GridFunction(fespace_hcurl) called u which I wish to solve for. I have added the relevant integrators, assembled and finalized. What is the simplest way to now solve this system?

Thank you for the help!