非结构网格下2D Riesz分数阶方程的Galerkin有限元方法  

Galerkin finite element method for 2D Riesz fractional differential equation based on unstructured meshes

作　　者：卜玮平 Bu Weiping(School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]湘潭大学数学与计算科学学院

出　　处：《纯粹数学与应用数学》2019年第2期169-181,共13页Pure and Applied Mathematics

基　　金：湖南省自然科学基金(2018JJ3491)

摘　　要：讨论了2D Riesz分数阶扩散方程的Galerkin有限元方法.基于非结构网格,采用Lagrange线性分片多项式作为基函数,详细描述了分数阶扩散方程的有限元实现.与现有方法相比,该方法有效地降低了计算成本,提高了刚度矩阵的精度.最后,数值算例验证了所提方法的有效性.Galerkin finite element method is developed for the two-dimensional Riesz fractional diffusion equations based on Dirichlet boundary conditions. The Lagrange linear piecewise polynomials is employed as the basis functions. Based on triangle unstructured meshes, the implementation of finite element method for fractional differential equations are described in detail. Comparing with the existing methods, the developed method efficiently reduces the computational cost and increases the accuracy of the stiffness matrix. Finally, some numerical tests are given to verify the effectiveness of the devised method.

关 键 词：Riesz分数阶扩散方程 有限元方法 非结构网格 

分 类 号：O178[理学—数学]