伪双曲方程的全离散修正H^1-Galerkin混合有限元方法(英文)  

Fully-discrete Modified H^1-Galerkin mixed Finite Element Methods of Pseudo-hyperbolic Equations

作　　者：赵利 方志朝[2] 

机构地区：[1]赤峰工业职业技术学院电子信息系,内蒙古赤峰024005 [2]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2014年第2期130-136,共7页Journal of Inner Mongolia University：Natural Science Edition

基　　金：Supported by National Natural Science Funds of China(No.11361035);the National Science Foundation of Inner Mongolia Province(No.2012MS0106);Scientific Research Projection of Higher Schools of Inner Mongolia(No.NJZY14013);Program of Higher Level Talents of Inner Mongolia University(No.135127)~~

摘　　要：利用修正的H1-Galerkin混合有限元方法求解了一类来源于神经传导过程的伪双曲型方程.在二维和三维空间下通过引入两个不同物理意义的辅助变量,将模型方程分解成两个一阶系统.对两个系统分别构造了全离散格式.在不需要验证LBB连续性条件和不需要限制逼近空间的条件下得到了最优阶误差估计.Modified H^1-Galerkin mixed finite element method is used to solve a class of second-order pseudo-hyperbolic equations arising in the modeling of nerve conduction process. The model equations in two and three space dimensions are splitted into two first-order systems by introducing two auxiliary variables with different physical meanings. The fully-discrete schemes are constructed for the two systems respectively. Optimal error estimates are derived without the LBB-consistency condition and the restriction on the approximating spaces.

关 键 词：修正的H^1-Galerkin混合有限元方法 全离散格式 伪双曲型方程 最优阶误差估计 

分 类 号：O242.21[理学—计算数学]