Numerical solvers of initial boundary value problems will exhibit instabilities and loss of accuracy unless carefully designed. The key property that leads to convergence is stability, which this thesis primarily deals with. By employing discrete differential operators satisfying a so called summation-by-parts property, it is possible to prove stability in a systematic manner by mimicking the continuous analysis if the energy has a bound. The articles included in the thesis all aim to solve the problem of ensuring stability of a numerical scheme in some context. This includes a domain decomposition procedure, a non-conforming grid coupling procedure, an application in high energy physics, and two methods at the intersection of machine learning and summation-by-parts theory.