论文标题
均匀的$ l^\ infty $ bunds用于旋转的pitaevskii方程的能源持稳定的高阶时间积分器
Uniform $L^\infty$-bounds for energy-conserving higher-order time integrators for the Gross-Pitaevskii equation with rotation
论文作者
论文摘要
在本文中，我们考虑了具有磁陷阱电势的总壁杆菌方程的连续连续盖尔金离散化，并且具有角动量旋转的搅拌电位。离散化基于时空中的有限元，并允许任意多项式顺序。首先在[O.中进行了分析。 Karakashian，C。Makridakis；暹罗J.肛门。 36（6）：1779-1807，1999]在没有潜在的术语和相应的先验误差估计中，在2D中得出。在这项工作中，我们在旋转的Gross-Pitaevskii方程的广义设置中重新审视了该方法，我们证明，对于2D和3D的相应数值近似值，我们证明了均匀的$ l^\ infty $ bugns，而无需空间网格尺寸和时间步长之间的数值近似值而没有耦合条件。在手头上，我们特别能够将先前的误差估计扩展到3D设置，同时避免人工CFL条件。
In this paper, we consider an energy-conserving continuous Galerkin discretization of the Gross-Pitaevskii equation with a magnetic trapping potential and a stirring potential for angular momentum rotation. The discretization is based on finite elements in space and time and allows for arbitrary polynomial orders. It was first analyzed in [O. Karakashian, C. Makridakis; SIAM J. Numer. Anal. 36(6):1779-1807, 1999] in the absence of potential terms and corresponding a priori error estimates were derived in 2D. In this work we revisit the approach in the generalized setting of the Gross-Pitaevskii equation with rotation and we prove uniform $L^\infty$-bounds for the corresponding numerical approximations in 2D and 3D without coupling conditions between the spatial mesh size and the time step size. With this result at hand, we are in particular able to extend the previous error estimates to the 3D setting while avoiding artificial CFL conditions.
