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