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.