Discontinuous boundary elements, such as constant elements, have been used in many engineering applications for years. In acoustics, the primary variables are sound pressure and normal particle velocity, and they can be defined at the center of each constant element. Since the acoustic variables do not need to be continuous across the element boundary, it is easy to write an algorithm to automatically refine the mesh by subdividing inside each element as frequency goes up. To take one step further, one may also choose to use a geometrically incompatible mesh, in which not only the primary variables but also the geometrical nodes do not need to be continuous across the element boundary. The main advantage is that a model can be quickly assembled from different sources without paying too much attention to the node-to-node continuity at junctions. As such, it is easy to add or remove a component at will to see its effect at the concept design stage. However, under certain circumstances, the incompatibility in mesh geometry may cause a problem. Any tiny gaps or overlays may affect the resonance frequencies if the muffler design relies on the natural frequency concept. In this paper, we study a few reactive and dissipative types of mufflers using both geometrically compatible and incompatible meshes. The objective is to provide some general guidelines on the use of incompatible meshes for muffler and silencer analysis.