Computable Error Estimates for Ground State Solution of Bose-Einstein   Condensates
  In this paper, we propose a computable error estimate of the Gross-Pitaevskii equation for ground state solution of Bose-Einstein condensates by general conforming finite element methods on general meshes. Based on the proposed error estimate, asymptotic lower bounds of the smallest eigenvalue and ground state energy can be obtained. Several numerical examples are presented to validate our theoretical results in this paper. 
Hehu Xie and Manting Xie
math.NA