def METHOD_NAME(degree):
    expected_conv = degree * 2
    len = 6
    errors = np.zeros(len)
    for i in range(len):
        m = CircleManifoldMesh(2**(i+3), degree=degree)
        mesh = ExtrudedMesh(m, layers=2**i, layer_height=1.0/(2**i))
        fs = FunctionSpace(mesh, "DG", 0)
        f = Function(fs).assign(1)
        # surface area is 2*pi*r*h = 2*pi
        errors[i] = np.abs(assemble(f*dx) - 2*np.pi)
    # area converges quadratically to 2*pi
    for i in range(len-1):
        assert ln(errors[i]/errors[i+1])/ln(2) > 0.98 * expected_conv