Articles | Volume 16, issue 6
https://doi.org/10.5194/se-16-457-2025
https://doi.org/10.5194/se-16-457-2025
Method article
 | 
20 Jun 2025
Method article |  | 20 Jun 2025

On the choice of finite element for applications in geodynamics – Part 2: A comparison of simplex and hypercube elements

Cedric Thieulot and Wolfgang Bangerth

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Cited articles

Arnold, D., Brezzi, F., and Fortin, M.: A stable finite element for the Stokes equation, Calcolo, XXI, 337–344, https://doi.org/10.1007/BF02576171, 1984. a
Barr, T. D. and Houseman, G. A.: Deformation fields around a fault embedded in a non-linear ductile medium, Geophys. J. Int., 125, 473–490, https://doi.org/10.1111/j.1365-246X.1996.tb00012.x, 1996. a
Bercovier, M. and Pironneau, O.: Error estimates for finite element method solution of the Stokes problem in the primitive variables, Numer Math., 33, 211–224, https://doi.org/10.1007/BF01399555, 1979. a
Boffi, D., Cavallini, N., Gardini, F., and Gastaldi, L.: Local mass conservation of Stokes finite elements, J. Sci. Comput., 52, 383–400, https://doi.org/10.1007/s10915-011-9549-4, 2012. a
Braess, D.: Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, Cambridge, ISBN 978-0-521705189, 2007. a, b, c
Short summary
One of the main numerical methods in geodynamics is the finite element method. Many types of elements have been used in the past decades in hundreds of publications. They usually fall under two categories: quadrilaterals and triangles. For the first time we compare results obtained with the most-used elements of each type on a series of geodynamical benchmarks and draw conclusions as to which are the best ones and which are to be preferably avoided.
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