Superconvergence of bi-k-Lagrange elements for eigenvalue problems

作者：Li, Z C; Chien, C S^*; Huang, H T; Jeng, B W

来源：Computer Physics Communications, 2009, 180(11): 2268-2282.

DOI：10.1016/j.cpc.2009.07.015

• Lagrange elements
• BEC
• Periodic potential
• Continuation methods

We study superconvergence of bi-k-Lagrange elements for parameter-dependent problems where k >= 2. We show that the superconvergence rate of the bi-k-Lagrange elements is two orders higher than that of the kth-order Lagrange elements. This is a significant improvement of the previous results [C.-S. Chien, H.T. Huang, B.-W. Jeng, Z.C. Li, Superconvergence of FEMs and numerical continuation for parameter-dependent problems with folds, Int. J. Bifurcation Chaos 18 (2008) 1321-1336]. which is only one order (or a half order) higher than that of the latter. Next, we apply the bi-k-Lagrange elements to the computations of energy levels and wave functions of two-dimensional (2D) Bose-Einstein condensates (BEC), and BEC in a periodic potential. Sample numerical results are reported.

• 出版日期2009-11
• 单位中山大学