Abstract: In this work we develop a numerical method for approximate so- lutions of the heat equation, based on the dual extremum principles of Noble and Sewell. We use the finite element method for discretization with cubic B- spline functions as basis in x and piecewise linear functions as basis in t. We exhibit a Hilbert space Y, a bilinear form S associated to it and we verify all the conditions of Lax-Milgram's lemma with which we get proof of existence and uniqueness of solution of the formulation we present. We prove also a convergence theorem and make an analysis of the numerical results obtained Ver menos