Lindner, MarkoMarkoLindnerSeifert, ChristianChristianSeifert2019-06-262019-06-262018-09GAMM Mitteilungen 3 (41): e201800013- (2018-09)http://hdl.handle.net/11420/2838We review approximation methods and their stability and applicability. We then focus on the finite section method and Galerkin methods and show that on separable Hilbert spaces either one can be interpreted as the other. In the end we demonstrate that well-known methods such as the finite element method and polynomial chaos expansion are particular examples of the finite section method; their applicability can therefore be studied via the latter.en1522-260820183e201800013Journal Article10.1002/gamm.201800013Other