对流占优扩散问题的特征动态有限元方法

The dynamic finite element method with characteristics for convection-dominated diffusion problems

将特征线方法与建立在变网格方法基础上的动态有限元空间相结合,对于二阶线性对流占优扩散问题构造了一种全离散特征动态有限元算法,证明了算法的稳定性,并给出收敛性分析与误差估计。证明了当Mh4/Δt有界时,能量模误差估计是最优的;而当Mh2/Δt有界时,L2模与能量模误差估计均达到最优,其中M为变网格的总次数,h和Δt分别为空间和时间网格参数。

The method of characteristics is combined with dynamic finite element spaces based on the moving grids method to ere- ate a fully discrete characteristic dynamic finite element procedure for the solution of second order linear convection-dominated dif- fusion problems. The procedure is proved to be stable. Convergence analysis and error estimates are established, which show that the error estimate in the energy norm is optimal when Mh^4/△t is bounded. Both the L^2-norm and the energy norm error estimate are optimal when Mh^2/△t is bounded, where M is the total number of grids-changing, h and △t are the spatial and temporal mesh parameters respectively.