ABSTRACT
Finite element methods are expected to continue to gain in popularity due to their key advantages such as that these methods can easily accommodate geometric irregularities, the element size can be easily varied, and the methods are easily adapted when material discontinuities are present. The finite element mesh obtained from the discretization step may be uniform if all the elements are of the same size, or it may be nonuniform to accommodate complex geometrical shapes. Since an exact solution for the differential equation may not be possible, a continuous function with unknown coefficients is used as an approximation of the solution for each element. The element equations obtained from the preceding step are linked together such that the continuity between the elements is maintained. As an illustration of how element equations are developed for a domain, one can consider a one-dimensional case of a long thin rod that has fixed boundary conditions and a continuous heat source along its axis.
