Find L2 projection of a given function in ngsolve

I'm finding L2 projection of a given function f on a finite element space Q.

Is there any function in Ngsolve do this job as in Fenics?

I also tried to write a find to find the L2-projection using its definition, but I met an error when finding the inverse matrix.

Could you please tell me how to fix this? Please see the attached file.
Thank you so much.

You have to do it following its definition. You are building some sub-block in a huge matrix, and the solver is telling you correctly that the big matrix is not invertible

Build and invert the matrix on a single space, then you can embed the single-space vectors in your product-space,

Joachim

Thank you so much. Could you please show me how to embed a single-space vectors in a product space?
I searched a tutorial from ngsolve documentation, but I couldn't find an example.

You can use an embedding matrix:
This embeds a vector of length b-a into a vector of length n, starting at index a.

some use-cases you can find here:
github.com/NGSolve/modeltemplates/blob/m...ates/NavierStokes.py

Joachim

Thank you so much for your clarification. I think ngsolve will be more user-friendly if it has an L2-projection built-in function.