This thesis reviews a method introduced by Larsson et al. for the incompressible Stokes’ problem. The method is devoted to computing bounds for the outputs of interest, as well as perform an adaptive mesh refinement. An error assessment technique is introduced in order to compute bounds for the outputs of interest. The technique goes through a split of the computation of the error in local problems. The results of the local problems allow to guarantee upper and lower bounds for the error energy norm and the outputs of interest. The pertinent adaptive mesh refinement is based on refinement indicators. They are used to evaluate the element contributions to the error. The elements that generate the most error in the output solution are subdivided. By these means, better precision is obtained in the output bounds by every iteration.