The main goal of the proposed research is to investigate and develop error estimators and mesh adaptation strategies within a discontinuous Galerkin (DG) formulation in order to reduce the computational cost, for a prescribed level of accuracy. We are interested in how multiwavelets (MWs) and their properties may shed new light on the adaptation process. This is motivated by the fact that MWs break any input apart into a hierarchy of low resolution data and subsequently finer details. Our error estimator makes use of MWs' properties while being local to the element, maintaining the parallel efficiency of the solver. Early tests on the one-dimensional viscous Burgers' equation show promising results. This work will be focused on a backward-facing step configuration to assess the performance of the method in higher dimensions.