Hey there,

The symbolic definition of (bi-) linearforms makes a lot of things easier.

But, I wonder whether one can also define a form including the nodal interpolant?

More specific: Consider the space of first order vector-valued H1 conforming elements, i.e., X = VectorH1(mesh, order=1).

The nodal interpolant I_h should now map a given (continuous) function f to a function f_h in the FE-space X, such that f(z) = f_h(z) for all nodes z in the mesh.

For two GridFunctions u and v in X, i can get the nodal interpolant of the cross-product denoted by I_h(u x v) quite easily (for example) by accessing the vectors of their nodal values.

But I struggle to use the nodal interpolant I_h in combination with test functions:

For example, is there a way to define a bilinear form like

<psi , curl( I_h(phi x v))>

in NgSolve?

Here again v denotes a GridFunction, while psi and phi denote a TrialFunction and a TestFunction, respectively. <.,.> denotes the L2 inner prduct.

Thanks in advance,

Best regards,

Carl