I am exploring DG time solvers. In particular, I have a simple diffusion equation
u_t - u_xx=0.
I want to use CG to discretize in space and upwinding DG in time. I think the TensorProductFespace is designed for such problem, but I failed to produce a working code. (the tutorial examples in tensorproducts are all explicit DG…)

Mathematically, we shall be able to solve the linear systems in time slabs, I don’t know whether this would be possible to realize in the current TensorProductFEspace. Can you help me with this? Many thanks!

As far as I know the TensorProductFESpace is not directly made for this.
In ngsxfem we have TensorProduct Space-Time spaces (also fitted), see e.g. here:

You can try it out without installation through binder here:

Your spacetime framework is exactly what I am looking for. I have an additional question: I want to test ideas in 1D first as my model is a bit complicated. But your framework seems only support dimension d>=2. Is there a easy way around?

I am thinking of directing work on a tensor-product quad slab domain, but some of the finite elements seems missing: I need two nonstandard fe spaces: Pk-in-x direction and P-0 in y-direction (time), also Pk-in-x direction and P-k-1 in y-direction.
Are these spaces already available in ngsolve core?

I just added 1D, at least for the scope of the examples that I’ve send you. You just need to update ngsxfem (master-branch). With that a script as attached works: https://ngsolve.org/media/kunena/attachments/743/1d.py .