We establish an a priori error analysis for the lowest-order Raviart-Thomas finite element discretisation of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence rates are obtained for the primal and dual variables as well as for the eigenvalue and energy approximations. In contrast to conformal approaches, which naturally imply upper energy bounds, the proposed mixed discretisation provides a guaranteed and asymptotically exact lower bound for the ground state energy. The theoretical results are illustrated by a series of numerical experiments.

翻译：针对非线性Gross-Pitaevskii特征值问题的最低阶Raviart-Thomas有限元离散化，我们建立了先验误差分析。对于原始变量、对偶变量以及特征值和能量逼近，均获得了最优收敛速率。与自然给出上能量界的共形方法不同，所提出的混合离散化方法为基态能量提供了保证且渐近精确的下界。一系列数值实验验证了理论结果。