fes = H1(mesh, order=2, dirichlet=“left|right”)

g = sin(y)

gfu = GridFunction(fes)

gfu.Set(g, BND)

the codes are from the i-tutorial 1.3 Dirichlet boundary conditions (1.3 Dirichlet boundary conditions — NGS-Py 6.2.2303 documentation)

Do we have the optimal estimate( trace inequality):

|gfu| _ {H^1(Domain)}

\leq C |g| _ {H^{1/2(boundary)}}

\leq Ch^{-1/2}|g| _ {L^2(Boundary)}?

**But,**

I think we just have

|gfu| _ {H^1(Domain)}

\leq Ch^{-1}|g| _ {L^2(Domain)}

\leq Ch^{-1}h^{1/2}|g|_ {L^infty(Boundary)}

\leq Ch^{-1}|g|_{L^2(Boundary)}

for the implementation in the Ngsolve codes