Local refinement enables us to concentrate computational resources in areas that need special attention, for example, near steep gradients and singularities. In order to use local refinement efficiently, it is important to be able to quickly estimate local error. FOSLS is an ideal method to use for this because the FOSLS functional yields a sharp a posteriori error measure for each element. This talk will discuss a strategy for determining which elements to refine in order to optimize the accuracy per computational cost on each level of refinement. Set in the context of a full multigrid algorithm, our strategy for the steep gradient case leads to a refinement pattern with nearly equal error on each element. Further refinement is essentially uniform, which allows for an efficient parallel implementation. In the case where singularities exist, the refinement pattern is modified to account for error reduction differences for elements that are close to the singularities. Numerical experiments will be presented.