The numerical method of partial differential equations is one of the most important branches in the field of computational mathematics. It has made great progress in the past half century. With the maturity of this research field, the research of various forms of application-driven methods and theories has become the general trend. Undoubtedly, basic research on calculation methods and algorithms is still an extremely important research topic in the ascendant. At the same time, the partial differential equations that accompany new applications raise many challenging problems that need to be solved urgently.