Sobolev方程的特征混合有限元方法

The CharacteristicsMixed Finite Element Method for Sobolev E quation

本文针对Sobolev方程提出了一种新型数值模拟方法—特征混合有限元方法 .该方法对方程的对流部分采用沿特征线的后退差分格式求解 ,以保证较小的截断误差限并避免了在流动的锋线前沿数值弥散现象的出现 ;对流动的扩散部分采用最低次混合元方法求解 ,以保证格式可同时逼近未知函数及伴随向量函数 .由于该方法中检验函数可取分片常数 ,此格式在某种意义上具有局部守恒性质 .通过严格的数值分析 ,建立了格式对待求函数及伴随向量的最优L2 误差分析理论 .

In this paper,we define a new numerical method called t he characteristic mixed finite element method for approximating the solution to Sobolev equation.We handle the convection part with backward difference scheme a long the characteristics,obtain much smaller timetrunction errors and avoid nu merical dispersion on the front of the peak curve of the flow:we use a lowest or der mixed finite element method to deal with the diffusion part,so this scheme c an approximate the unknow function and its following vector with high accuracy a t the same time.Piecewise constants are then in the test function space,so mass is cinserved element by element in the discrete level.The optimal L 2 error estimate for the unknown function and its following vector are presented.