We present an effective adaptive procedure for the numerical approximation of the steady-state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and consists of a combination of a novel adaptive finite element mesh refinement technique, which does not rely on any a posteriori error estimates, and a recently proposed new gradient flow. Numerical tests show that this strategy is able to provide highly accurate results, with optimal convergence rates with respect to the number of degrees of freedom.

中文翻译：

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Gross-Pitaevskii方程的基于能量的自适应梯度流有限元离散化

我们为稳态Gross-Pitaevskii方程的数值逼近提供了一种有效的自适应程序。我们的方法仅基于能量最小化，并且由不依赖于任何后验误差估计的新型自适应有限元网格细化技术和最近提出的新梯度流组成。数值测试表明，该策略能够提供高度准确的结果，并且相对于自由度数而言具有最佳收敛速度。