Abstract:

The method of characteristics is combined with dynamic  finite element spaces based on the moving grids method to create a fully discrete characteristic dynamic finite element procedure for the solution of  second order linear convectiondominated diffusion 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 Mh⁴／Δt is bounded. Both the L²-norm and the energy norm error  estimate are optimal when  Mh²／Δt is bounded, where M is the total number of gridschanging. h and Δt are the spatial and temporal mesh parameters respectively. 

Key words: dynamic finite element spaces； characteristic method；  negative-norm estimate； convection-dominated diffusion problems
〖BT1〗〖STFZ