非线性守恒律高阶谱粘性法的收敛性  

Convergence of super spectral viscosity methods for nonlinear conservation laws

作　　者：纪园园[1] 李会元[2] 

机构地区：[1]上海大学理学院,上海200444 [2]中国科学院软件研究所,北京100190

出　　处：《应用数学与计算数学学报》2011年第2期224-234,共11页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(10971212)

摘　　要：讨论守恒型方程周期边界问题的高阶谱粘性方法逼近解的收敛性.在逼近解一致有界的假设下,通过建立其高阶导数的上界估计,证明了高阶谱粘性方法逼近解具有同二阶谱粘性方法逼近解相类似的高频衰减性质.以此为基础,用补偿列紧法证明了高阶谱粘性方法逼近解收敛于守恒型方程的物理解.The convergence of the super spectral viscosity（SSV） methods for periodic nonlinear conservation laws is studied.Based on the hypothesis that the SSV solutions are uniformly bounded,the upper bound estimates on the high-order derivatives of the SSV solutions are first established.The SSV methods are then shown to possess some high-frequency decaying properties,just as the second order spectral viscosity method.Finally,it is proven,by the compensated compactness method,that the bounded SSV solutions converge to the physical solutions.

关 键 词：守恒型方程 高阶谱粘性方法 高频衰减 收敛性 

分 类 号：O241.82[理学—计算数学]