In this thesis we conduct a numerical study of the 1D viscous Burgers' equation and several Reduced Order Models (ROMs) over a range of parameter values. This study is motivated by the need for robust reduced order models that can be used both for design and control. Thus the model should first, allow for selection of optimal parameter values in a trade space and second, identify impacts from changes of parameter values that occur during development, production and sustainment of the designs. To facilitate this study we apply a Finite Element Method (FEM) and where applicable, the Group Finite Element Method (GFE) due its demonstrated stability and reduced complexity over the standard FEM. We also utilize Proper Orthogonal Decomposition (POD) as a model reduction technique and modifications of POD that include Global POD, and the sensitivity based modifications Extrapolated POD and Expanded POD. We then use a single baseline parameter in the parameter range to develop a ROM basis for each method above and investigate the error of each ROM method against a full order "truth" solution for the full parameter range.