Recent results in the systematic derivation and convergence of SPH
  This paper presents the derivation of SPH from principles of continuum mechanics via a measure-based formu- lation. Additionally, it discusses a theoretical convergence result, the extensions achieved from previous works and the current limitations of the proof. In support of the theoretical result, numerical experiments show that SPH converges with respect to the Wasserstein distance as the number of particles grows to infinity. Convergence is still observed for those numerical experiments which are not covered by the hypotheses of the theoretical result. The latter finding suggests that it should be possible to prove the theoretical result under weaker conditions. 
Iason Zisis and Joep H.M. Evers and Bas van der Linden and Manh Hong   Duong
math.NA math-ph math.MP