A simple finite-element algorithm is derived for the solution of the one-dimensional advection-diffuaon transport equation. Local interpolation functional are obtained for each subdomain, or element, by using linear basis functions. The integral form of the finite-element algorithm is evaluated by using hypermatrices and a natural coordinate system. Assemblage over two adjacent elements gives the tridiagonal recursion relation for chapeau functions. By time-splitting either a two-or a three-dimensional equation into a series of one-dimensional equations and by using the basic one-dimensional finite-element algorithm, multidimensional problems can be solved with little additional programming complexity or storage.