The simulation of ow- and vibration-induced sound generation phenomena poses a number of problems due to large scale disparities. In aeroacoustics for low Mach-number ows small features in a slow ow generate acoustic disturbances which propagate away at the speed of sound. e characteristic acoustic wave lengths are typically large compared to the domain of the ow. Mechanical vibrations at low frequencies of up to about kHz generate sound with wave lenghts, which are sometimes even larger than the vibrating structures. Both phenomena require the use of special numerical methods to cope with.The preceding arguments make the need for di erent discretizations in different parts of a computational domain quite clear. e standard nite element method (FEM) is not well-suited to overcome these problems, due to its need for conforming meshes. erefore the Mortar FEM, which is a non-overlapping domain decomposition method and permits non-matching grids at interfaces, gets applied in this thesis. With this method also the generation of computational models becomes much more exible, since subdomain grids can be generated independently and can therefore be adapted to the physical needs in di erent parts of the domain.By allowing non-matching grids the approximate solutions have to be transferred across interfaces in an appropriate way. e coupling integrals arising at these interfaces need to be evaluated with respect to di erent meshes and therefore sophisticated mesh intersection algorithms have to be implemented.Similar algorithms have to be developed for the interpolation of aeroacoustic sound sources. e sources get computed from velocity elds according to Lighthill's acoustic analogy on ne computational uid dynamics (CFD) meshes. A erwards they get interpolated to relatively coarse acoustic grids in order to reduce the problem sizes.The developed algorithms get applied to a number of test cases. For aeroacoustics a cylinder in cross- ow and the setup of an edge-tone are investigated. For vibroacoustics the Mortar FEM gets applied to the cases of an electrodynamic loudspeaker and to piezoelectric patches for active noise damping.