Abstract
Abstract In this study we propose a novel adaptive finite element method for the ground state solution of Bose-Einstein Condensates (BEC). Different from the classical adaptive scheme applied to BEC which needs to solve a nonlinear eigenvalue model directly on each adaptive finite element space, our scheme requires to solve a linear elliptic boundary value problem on current adaptive space and a nonlinear eigenvalue model on a quite low-dimensional correction space. Further, the linear elliptic boundary value problem is solved by adaptive multigrid iterations. Since there is no nonlinear eigenvalue model to be solved directly on the adaptive spaces, the solving efficiency can be improved evidently. In addition, the convergence analysis of the proposed adaptive algorithm are derived numerically and theoretically.
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