Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve. Therefore, approximations to the FS equations are used, especially when modeling an ice sheet on long time spans. Here, we report a combination of an approximation with the FS equations that allows simulating the dynamics of ice sheets over long time spans without introducing artifacts caused by application of approximations in parts of the domain where they are not valid.