\(C^1\) error estimation on the boundary for an exterior Neumann problem in \(\mathbb{R}^3\) (Q5943704)

The paper deals with approximation on the boundary of \(u\) and \(Du\), where \(u\) is given by \[ \begin{cases} -\Delta u=0 & \text{in }^e\Omega,\\ \frac{\partial u}{\partial v}=g & \text{on }\partial \Omega,\\ u=0(1) & \text{at } \infty.\end{cases} \] The author gives a \(C^1\) error approximation of \(u\) and \(Du\) on the boundary by using a full piecewise linear discretization.