中文摘要：

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.

英文摘要：

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.