【摘要】 本文的主要目的是讨论在各向异性网络剖分下四阶特征值问题的双三次Hernmite有限元逼近。由于该网格不同于传统有限元方法中的正则性剖分或拟一致剖分,在理论分析过程中不能直接使用Sobolev插值理论。本文将利用新的技巧,导出与传统网格剖分下相同的最优误差估计。更多还原

【Abstract】 The aim of this paper is to investigate the approximation to the fourth order eigen- value problem with cubic Hermite elements on anisotropic meshes. Because of the difference between anisotropic meshes and regular condition or uniform assumption used in classical finite element meth- ods, the Sobolev interpolate theorem can not be used directly in the theoretical analysis. The optimal error estimates will be derived through some novel approaches.更多还原