Multidomain pseudospectral methods for nonlinear convection-diffusion equations

Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method, but the nonlinear term is collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval. Appropriate base functions are introduced so that the matrix of the system is sparse, and the method can be implemented efficiently and in parallel. The stability and the optimal rate of convergence of the methods are proved. Numerical results are given for both the single domain and the multidomain methods to make a comparison.     

非线性对流-扩散方程的多区域拟谱方法

提出了非线性对流-扩散方程的多区域拟谱方法．在每个子区间上,该格式整体上按Legendre－Galerkin方法形成,但对于非线性项采用在 Legendre/Chebyshev－Gauss-Lobatto点上的配置法处理．通过选取适当的基函数,使得系数矩阵稀疏,并且可以并行计算,提高运算效率．给出了该方法的稳定性和收敛性分析,获得了按L2-模的最佳误差估计．最后给出单区域和多区域方法的数值算例,并加以比较．     

非线性守恒律高阶谱粘性法的收敛性

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.