ABSTRACT
From the engineer’s viewpoint, the objective in the finite element method is to establish an approximate solution to the boundary value problem that is sufficiently accurate for engineering design. That is, one hopes that the error can be made reasonably small by an analysis using the number of elements that can be handled by the available computer. From the mathematician’s viewpoint, the objective is to establish a numerical procedure that ensures that any prescribed measure of error can be made as small as desired by taking enough elements, even if such calculations cannot actually be performed, that is, the mathematician seeks proof of convergence. The engineer seeks to achieve small error within the available capacity of the computer.
