一类三维拟线性双曲型方程交替方向有限元法  

GALERKIN ALTERNATING-DIRECTION METHODS FOR A KIND OF THREE-DIMENSIONAL QUASI-LINEAR HYPERBOLIC EQUATIONS

作　　者：来翔[1] 袁益让[1] 

机构地区：[1]山东大学数学学院,济南250100

出　　处：《计算数学》2010年第1期15-36,共22页Mathematica Numerica Sinica

基　　金：山东省自然科学基金青年项目(批准号:Q2007A03)

摘　　要：对一类一般的三维拟线性双曲型方程通过转化二阶时间导数得到关于一阶时间导数的耦合方程组,然后进行离散得到交替方向有限元格式,应用微分方程先验估计的理论和技巧得到了最优阶H^1-模和L^2-模误差估计,并给出了数值算例,数值结果和理论分析得到很好的吻合.A kind of second-order three-dimensional quasi-linear hyperbolic equation is firstly transformed into a system of first-order equations,then the Galerkin alternating-direction procedure for the system is derived.The optimal order estimates inH^1 norm and L^2 norm of the procedure are obtained respectively by using the theory and techniques of priori estimate of differential equations.The numerical experiment is also given to support the theoretical analysis.Comparison the results of numerical example with the theoretical analysis shows they are uniform.

关 键 词：双曲型方程 一阶方程组 交替方向有限元方法 收敛性分析 数值试验 

分 类 号：O241.82[理学—计算数学]