[lzhaok6]

Originally Posted by FMDenaro

Why do not use an initial smooth function like a gaussian centered at x=0? you can just let to evolve towards +/- x direction. This way you can check the orde of accuracy in time and space.

Thank you very much for your suggestion. I've tried to impose a sin wave on the boundary. However, the observed order of accuracy is still not as expected. The L2 norm of error is like: 0.0032 when CFL=0.1; 0.0031 when CFL=0.2; 0.0055 when CFL=0.4; 0.0051 when CFL=0.8.

I think the overall accuracy is influenced by the dispersion of spatial discretization of finite element method. The dispersion would increase as the mismatch between the numerical speed and physical speed is enlarged (i.e. when CFL deviates from 1). However, I'm not sure if this explanation is theoretically sound.