Trialfunction does not support BND-forms, maybe a Trace() operator is misssing

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1

Hello everyone ,

I am trying to calculate an integral on the dirichlet boundary, however for some reason I keep getting an error saying “Trialfunction does not support BND-forms, maybe a Trace() operator is misssing”

My geometry is and function space is:

[code] from netgen.geom2d import SplineGeometry
geo = SplineGeometry()
geo.AddRectangle( (0, 0), (0.41, 2), bcs = (“b”, “r”, “t”, “l”))
geo.AddCircle ( (0.2, 1.8), r=0.05, leftdomain=0, rightdomain=1, bc=“cyl”)
mesh = Mesh(geo.GenerateMesh(maxh=0.08))
mesh.Curve(3)

V = VectorH1(mesh,order=3, dirichlet=“t|cyl|l|r”)
Q = H1(mesh,order=2)
X = FESpace([V,Q])
u,p = X.TrialFunction()
v,q = X.TestFunction()

h = specialcf.mesh_size
n = specialcf.normal(2)[/code]

and I want to impose Dirichlet boundary conditions only on the “t” boundary weakly. For that I need to calculate following:

a += SymbolicBFI(-nu*InnerProduct(grad(u)*n,v) -nu*InnerProduct(grad(v)*n,u) +nu*alpha/h*InnerProduct(u,v), definedon=mesh.Boundaries("t"))

but this calculation gives me the above-mentioned error.

Anyone can see what is going on here?

Thanks in advance.

2

Hi noname,

You want the gradient of volume elements (aligned to boundary elements) evaluated. The SymbolicBFI on the boundary however only has the information of the boundary elements. Use the option “skeleton=True” combined with “VOL_or_BND=BND” to obtain access to the gradients of the aligned volume elements.

Best,
Christoph

3

For your mentioned purpose, if I write

a = BilinearForm(-InnerProduct(Grad(u)*n,v)
                 *ds("t")).Assemble()

error:
Trialfunction does not support BND-forms, maybe a Trace() operator is misssing.

how to fix?

I think if i use

a = BilinearForm(-InnerProduct(Grad(u).Trace()*n,v)
                 *ds("t")).Assemble()

I get the tangential derivative as said in
https://docu.ngsolve.org/latest/how_to/howto_traceoperator.html?highlight=trace
However, I want get the usual gradient firstly, then integral on the boundary.