Finite elements; perhaps no other family of approximation methods has had
a greater impact on the theory and practice of numerical methods during the
twentieth century. Finite element methods have now been used in virtually every
conceivable area of engineering that can make use of models of nature characterized
by partial differential equations. There are dozens of textbooks, monographs,
handbooks, memoirs, and journals devoted to its further study; numerous
conferences, symposia, and workshops on various aspects of finite element
methodology are held regularly throughout the world. There exist easily over one
hundred thousand references on finite elements today, and this number is growing
exponentially with further revelations of the power and versatility of the method.
Today, finite element methodology is making significant inroads into fields in which
many thought were outside its realm; for example, computational fluid dynamics. In
time, finite element methods may assume a position in this area of comparable or
greater importance than classical difference schemes which have long dominated the
subject.