On the choice of finite element for applications in geodynamics – Part 2: A comparison of simplex and hypercube elements - C. Thieulot; W. Bangerth (Solid Earth)
Many geodynamical models are formulated in terms of the Stokes equations that are then coupled to other equations. For the numerical solution of the Stokes equations, geodynamics codes over the past decades have used essentially every finite element that has ever been proposed for the solution of this equation, on both triangular/tetrahedral (“simplex”) and quadrilaterals/hexahedral (“hypercube”) meshes. However, in many and perhaps most cases, the specific choice of element does not seem to have been the result of careful benchmarking efforts but based on implementation efficiency or the implementers' background.