有限元理论中的科学研究方法

Scientific Research Methods in Finite Elements Theory

有限元方法是目前计算数学最活跃的分支之一 ,关于它的基础数学理论和数值实现广泛受到理论界和工程界的重视 .本文为作者在对有限元方法的学习研究中 ,结合自然辩证法、科学技术革命与当代社会、马克思主义哲学原理课程的学习 ,对该领域中几对范畴如连续与离散、有限与无限、部分与整体、协调与非协调、空间与时间复杂度之间关系的认识和体会 .揭示了科学方法论对该领域研究探索中的指导作用 .

Finite elements method is an active branch of compu ting mathematics. Scientific researchers and engineers pay more attention to its mathematical foundation and numeric computation. This paper gives the philosoph y principles of the methods in this field, demonstrates the relations between fi nite and infinite, continues and discrete, part and integration , conform and nonconform, space and time etc. These ideas will give guidance to our research work.