Ultraconvergence for averaging discontinuous finite elements and its applications in Hamiltonian system

This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations.When k is even,the averaging numerical flux (the average of left and right limits for the discontinuous finite element at nodes) has the optimal-order ultraconvergence 2k + 2.For nonlinear Hamiltonian systems (e.g.,Schro¨dinger equation and Kepler system) with momentum conservation,the discontinuous finite element methods preserve momentum at nodes.These properti...     

三角形线元的校正法

有限元校正是近年开始研究的一种高精度算法,从已得结果来看它已显示了许多优点:1.它比差分法校正简单,由于在内积中使用分部积分,降低了要逼近的导数阶次;2.校正法的证明虽比外推法复杂,但用直接法求解时计算量却少些,而且数值试检表明它的计算精度更高些。Mackinnon-Carey研究过有限元的校正,但其证明模仿差分法,某些优点未能显示出来。陈传森—张智江用有限元的论证技巧讨论了一维问题。文研究了双一次元的校正。本文考虑矩形上的三角形线元,关于更一般的三角形剖分将在另文中讨论。     

THE ACCELERATED SEARCH-EXTENSION METHOD FOR COMPUTING MULTIPLE SOLUTIONS OF SEMILINEAR PDEs

In this paper, we propose an accelerated search-extension method （ASEM） based on the interpolated coefficient finite element method, the search-extension method （SEM） and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems, but also reduces the expensive computation greatly. The numerical results in I-D and 2-D cases will show the efficiency of our approach.