The previous chapter has discussed the solution of partial differential equations using the classical finite difference approach. This method of solution is most appropriate for physical problems that match to a rectangular boundary area or that can be easily approximated by a rectangular boundary. One such class of PDEs is initial value problems in one spatial variable and one time variable. Other selected problems in two spatial dimensions are also amendable to this approach and selected examples are given in the previous chapter.
A large class of PDEs, however, involve spatial dimensions not confined to a rectangular geometry and for such problems the more recently developed finite element (FE) approach is in many cases much more appropriate. As in the previous chapter some of the important theory underlying the FE method will be discussed and selected computer code developed to implement a selected subset of FE approaches. The code is then used to illustrate the solution of selected PDEs by the FE approach.