  It is well understood that boundary conditions (BCs) may cause global radial
basis function (RBF) methods to become unstable for hyperbolic conservation
laws (CLs). Here we investigate this phenomenon and identify the strong
enforcement of BCs as the mechanism triggering such stability issues. Based on
this observation we propose a technique to weakly enforce BCs in RBF methods.
In the case of hyperbolic CLs, this is achieved by carefully building RBF
methods from the weak form of the CL, rather than the typically enforced strong
form. Furthermore, we demonstrate that global RBF methods may violate
conservation, yielding physically unreasonable solutions when the approximation
does not take into account these considerations. Numerical experiments validate
our theoretical results.
