NDSolveValue for Laplace equation not converging to analytic solution

Question

I'm solving Laplace equation $\nabla^2 \phi = 0$ with BC's $\phi_x(x=\pm 1) = 0,\, \phi_y(y=-h) = 0$ with a specified BC along the circular arc $x^2 + (-1 + y)^2 = 4$, which I call $\Gamma$ (so the domain $\Omega$ is like a rectangular box with the circular arc $\Gamma$ as the lid).

What I've done is taken the analytic solution $\phi_A = \cos(\pi m (x + 1)/2) \cosh(\pi m (y + h)/2) : m \in \mathbb{N}$ and evaluated its normal derivative on $\Gamma$, and then set this as a Neumann boundary condition for the top lid. Since this does not give a unique solution (no Dirichlet BC) I also give the PDE the BC $\phi = \phi_A(1,\Gamma(x=1))$. However, the numerical solution does not converge to the analytic solution. Code is supplied below, which shows the domain $\Omega$ for clarity.

h = 2;
r = 2;
yp = 1;
m = 1;
Ω = ImplicitRegion[-1 <= x <= 1 && -h <= y <= 2 && ! (x^2 + (y - yp)^2 <= r^2), {x, y}];
Region[Ω]
ϕA = Cos[(π m)/2 (x + 1)] Cosh[(π m)/2 (y + h)];
g = ϕA /. y -> -Sqrt[r^2 - x^2] + yp /. x -> 1;
dnϕA = Grad[ϕA, {x, y}]. ({x, y}/Sqrt[x^2 + y^2]);
dnϕΓA = dnϕA /. y -> -Sqrt[r^2 - x^2] + yp;
op = Laplacian[ϕD[x, y], {x, y}];
ΓNV = NeumannValue[dnϕA, x^2 + (y - yp)^2 == r^2];
Γ = {DirichletCondition[ϕD[x, y] == g, x == 1 && y == -Sqrt[r^2 - 1^2] + yp]};
Needs["NDSolve`FEM`"]
mesh = ToElementMesh[Ω, MaxCellMeasure -> 0.01];
mesh["Wireframe"]
ϕ = NDSolveValue[{op == ΓNV, Γ}, 
ϕD, {x, y} ∈ mesh, InterpolationOrder -> 3];
Plot3D[{ϕ[x, y], ϕA}, {x, y} ∈ Ω, 
 AxesLabel -> {"x", "y", "ϕ"}]

Answer 1

egwene sedai and Alex Trounev posted the solution in the comments. I was using the wrong normal vector to the surface when evaluating the NeumannCondition.

Edit: my normal derivative to the circular arc $\Gamma$ assumed the center was the origin. After recognizing the center was intentionally above the origin, the normal vector should be changed to

({x, y - yp}/Sqrt[x^2 + (y - yp)^2])