Abstract
Geodynamical simulations over the past decades have widely been built on quadrilateral and hexahedral finite elements. For the discretization of the key Stokes equation describing slow, viscous flow, most codes use either the unstable Q1×P0 element, a stabilized version of the equal-order Q1×Q1 element, or more recently the stable Taylor-Hood element with continuous (Q2×Q1) or discontinuous (Q2×P-1) pressure. However, it is not clear which of these choices is actually the best at accurately simulating "typical"geodynamic situations. Herein, we provide a systematic comparison of all of these elements for the first time. We use a series of benchmarks that illuminate different aspects of the features we consider typical of mantle convection and geodynamical simulations. We will show in particular that the stabilized Q1×Q1 element has great difficulty producing accurate solutions for buoyancy-driven flows - the dominant forcing for mantle convection flow - and that the Q1×P0 element is too unstable and inaccurate in practice. As a consequence, we believe that the Q2×Q1 and Q2×P-1 elements provide the most robust and reliable choice for geodynamical simulations, despite the greater complexity in their implementation and the substantially higher computational cost when solving linear systems.
| Original language | English |
|---|---|
| Pages (from-to) | 229-249 |
| Number of pages | 21 |
| Journal | Solid Earth |
| Volume | 13 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 28 Jan 2022 |
Bibliographical note
Funding Information:tion under award EAR-1550901. Additional support was provided by the National Science Foundation through awards EAR-1550901 and OAC-1835673 as part of the Cyberinfrastructure for Sustained Scientific Innovation (CSSI) program, as well as EAR-1925595.
Funding Information:
Acknowledgements. The authors thank Dave May, Matthew Knep-ley, and an anonymous reviewer for their comments that have helped improve the paper. We thank the Computational Infrastructure for Geodynamics (http://geodynamics.org, last access: 21 June 2021) for their support of the ASPECT code. Cedric Thieulot also wishes to thank Riad Hassani for his help at the very early stages of this work. Wolfgang Bangerth gratefully acknowledges support by the National Science Foundation.
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Funding
tion under award EAR-1550901. Additional support was provided by the National Science Foundation through awards EAR-1550901 and OAC-1835673 as part of the Cyberinfrastructure for Sustained Scientific Innovation (CSSI) program, as well as EAR-1925595. Acknowledgements. The authors thank Dave May, Matthew Knep-ley, and an anonymous reviewer for their comments that have helped improve the paper. We thank the Computational Infrastructure for Geodynamics (http://geodynamics.org, last access: 21 June 2021) for their support of the ASPECT code. Cedric Thieulot also wishes to thank Riad Hassani for his help at the very early stages of this work. Wolfgang Bangerth gratefully acknowledges support by the National Science Foundation.