The FOSLS approach to partial differential equations of second order is based on the minimization of a functional that in many cases is equivalent to a 'nice' norm (like the H^1 norm). This makes multigrid a suitable method to solve the discrete minimization problem. In many applications it is not feasible to solve the discrete problem on a uniform grid due to limited availability of computing resources time. Hence adaptive methods need to be developed to solve the discrete minimization problem up to a given accuracy.
The FOSLS functional is a natural global error measure, in fact it has the property that it is equal to zero at the minimum. We will show how the FOSLS functional provides us with an a posteriori error estimator, that can be used to generate adaptively refined grids.