Cristina Bacuta
University of Delaware, Newark, DE, USA

When introducing discretization of boundary value problem solutions in a first course on numerical methods, the traditional way is to start with a finite difference approach followed by a separate finite element approach. In this talk, we describe a different way that emphasizes on the connections between the two methods and the advantage of their simultaneous analysis. For a model problem, we write the finite difference and the finite element systems such that the two corresponding linear systems have the same stiffness matrices. then, we compare the right hand side load vectors for the two methods. Using the connection between a Green function and the linear finite element basis functions, we find an explicit form of the inverse of the stiffness matrix. We simplify the proofs for the standard finite differences error estimates in the discrete infinity norm and the energy norm. This is joint work with Constantin Bacuta.