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 the ground state solution of the Bose–Einstein condensate by the general conforming finite element method on general meshes. Based on this error estimate, the asymptotically lower and upper bound for the smallest eigenvalue and ground state energy can be calculated. Several numerical examples are presented to validate the theoretical results in this paper.

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