In this talk, we consider some interesting PDEs, for example, the Allen-Cahn equation, Cahn-Hilliard equation, Keller-Segel equation and Fokker-Planck equation. We developed numerical methods for those PDEs in Eulerian and Lagrangian coordinates respectively. Some results about stability and error analysis will be presented for our numerical schemes. Interesting numerical experiments will also be shown to validate the stability and accuracy of our numerical methods.
