A Galerkin method for the forward-backward heat equation

Abstract

In this paper a new variational method is proposed for the numerical approximation of the solution of the forward-backward heat equation. The approach consists of first reducing the second-order problem to an equivalent first-order system, and then using a finite element procedure with continuous elements in both space and time for the numerical approximation. Under suitable regularity assumptions, error estimates and the results of some numerical experiments are presented.