The finite element method for computing the ground states of the dipolar Bose-Einstein condensates

A finite element approximation for computing the ground states of the dipolar Bose-Einstein condensates with a nonlocal nonlinear convolution term is presented in one dimension. Following the idea of the imaginary time method, we compute the ground state finite method solution of the Bose-Einstein condensates by solving a nonlinear parabolic differential-integral equation. Theoretical analysis is given to show the existence and convergence of this finite method solution. Numerical results are given to verify efficiency of our numerical method. (C) 2014 Elsevier Inc. All rights reserved.