The History Of Finite Element Method In Perspective Of Context

Computational mathematics is a very important branch of modern mathematics, but the research of the history of computational mathematics is far from sufficient in China. This paper studies the history of finite element method, which is a mature and effective method of computational mathematics, and analyzes the history of finite element method from the perspective of context.The history of finite element method can be divided into 3 stages: invention(1943), development(1944-1960), and complement(1961-1990's). The combined effects of external force made finite element method birth. In 1943, Courant published mathematical paper "Variational methods for the solution of problems of equilibrium and vibration" and Argyris achieved a major breakthrough in the engineering marked the birth of the finite element method.In the early history of finite element method (1944-1960), people formed a complete algebraic expressions, started the study of divide of unit and chose of unite type, and the convergence of finite element method was initially proved. In 1960, Clough invented the name "Finite Element Method," which indicated the end of early history of finite element method.The latter history of finite element method (1961 - 1990s) has 2 clues: in China and abroad. The latter development of finite element method abroad is: the concise, complete algebraic expression of finite element method was established, and common commercial packages were created; the application of the finite element method extended outside the scope of the structural mechanics, and the curved unit was introduced, the convergence of solutions was further researched, and error estimation theory system was established. In China, Feng Kang invented finite element method independently. In 1965, he published paper "Difference Scheme based on Variation Principle" ,which indicated the birth of finite element method in China. In his article, Fengkang gave the expression of finite element method under certain conditions, created the " Feng theorem",and initially proved the convergence of the finite element method. Although Feng Kang's method was immature, his work was great. Experts and scholars at home and abroad and the state leaders have highly comment on his achievement.As a scientific language, finite element method can be classified as three aspects: morphology, semantics and pragmatics. These aspects of finite element method are unified on the basis of context. The generalized context of finite element method includes 4 factors: external context, scientists, agencies and the objects of study. They influenced the history of finite element method all the time, so the development of finite element method depends on specific context, that's why we study the history of finite element method from the perspective of context.