带有齐次混合边界条件的特征值问题的局部和并行有限元算法-计算数学专业论文.docxVIP

PAGE PAGE 11 PAGE PAGE 10 Introduction In recent years, more and more scholars study the numerical solution of partial dif- ferential equations, and finite element method is applied widely in the numerical solution of partial differential equations. In order to improve it’s efficiency many scholars made a lot of work and established many algorithms, for example, the adaptive finite element methods (see [11],[15]), multi-scaled method (see [7],[9],[27]), local and parallel algorithms (see [12],[13],[22],[23]), spectral method (see [14]) and etc. In [22] Xu and Zhou established local and parallel algorithm, which has gradually become the hot topic for numerical solution of partial differential equations. This method has been used and developed by many scholars. And it has been successfully applied to Stokes equations (see [12], [13], [17]), elliptic boundary value problems (see [22]) and eigen- value problems (see [5], [9] and [23]) and etc. For the eigenvalue problems, many scholars have done many meaningful researches. Xu and Zhou established some local and parallel algorithms for eigenvalue problems, see [23]. Dai and Zhou established local and parallel algorithms for quantum eigenvalue prob- lems, see [9]. Based on shifted-inverse power method, Bi et al. established new local and parallel finite element three-scale schemes for singular eigenvalue problems with Dirichlet boundary value condition, see [5]. All above researches imply that local and parallel algo- rithm is an effective method for numerical solution of eigenvalue problems. . As we know, there has no researches about local and parallel algorithms for eigen- value problems with homogeneous mixed boundary conditions. Based on the work of [9] and [5], this paper will discuss local and parallel algorithms for eigenvalue problems with homogeneous mixed boundary conditions, see Schemes 1 and 2. The main features of this paper are as follows: （1）A priori estimate is proposed for eigenvalue problems with