一类神经传导方程的变网格有限元方法及数值分析

Time-Dependent Variable Grid Finite Element Method for the Nerve Conductive Equarions

研究在神经传播过程中的一类非线性拟双曲方程的初边值问题,对二维情形应用常规变换,提出了两种变网格有限元格式,最后通过细致的分析和估计得到了最佳阶的H1和L2 模误差估计结果,并且第二种格式使时间精度提高一阶,最后对第一种格式作了数值实验,指明方法是高效可行的．

In this paper,time-dependent variable grid finite element method is introduced and analyzed for approximating the solutions of the nerve conductive equarion in 2-space vari- ables. The optimal error estimates in H^1 and L^2 are obtained,a numarical experiment given in the end proves that the method is practicable.