We establish an a priori error analysis for the lowest-order Raviart–Thomas finite element discretization 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 conforming approaches, which naturally imply upper energy bounds, the proposed mixed discretization provides a guaranteed and asymptotically exact lower bound for the ground state energy. The theoretical results are illustrated by a series of numerical experiments.

中文翻译：

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Gross–Pitaevskii 特征值问题的混合有限元：先验误差分析和保证的能量下限


我们为非线性 Gross-Pitaevskii 特征值问题的最低阶 Raviart-Thomas 有限元离散化建立了先验误差分析。获得原始变量和对偶变量以及特征值和能量近似的最佳收敛速率。与自然意味着能量上限的一致方法相比，所提出的混合离散化为基态能量提供了有保证且渐近精确的下界。一系列数值实验说明了理论结果。