Elliptic Equations

A brief review is given of the literature on numerical methods for elliptic problems as related to the ideas introduced by Courant, Friedrichs and Lewy in the fundamental paper published in Math. Ann. 100, 32 (1928). The discussion shows how the finite-difference methods have subsequently been extended and applied to higher order elliptic problems and how the recent literature has reported methods for solving large algebraic systems. In addition, there is a discussion of the relation between the Dirichlet problem and the problem of the random walk.