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Title: On the choice of finite element for applications in geodynamics
Abstract. Geodynamical simulations over the past decades have widely beenbuilt on quadrilateral and hexahedral finite elements. For thediscretization of the key Stokes equation describing slow, viscousflow, most codes use either the unstable Q1×P0 element, astabilized version of the equal-order Q1×Q1 element, ormore 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 isactually the best at accurately simulating “typical” geodynamicsituations. Herein, we provide a systematic comparison of all of theseelements for the first time. We use a series of benchmarks that illuminate differentaspects of the features we consider typical of mantle convectionand geodynamical simulations. We will show in particular that the stabilizedQ1×Q1 element has great difficulty producing accuratesolutions for buoyancy-driven flows – the dominant forcing formantle convection flow – and that the Q1×P0 element istoo unstable and inaccurate in practice. As a consequence, webelieve that the Q2×Q1 and Q2×P-1 elementsprovide the most robust and reliable choice for geodynamical simulations,despite the greater complexity in their implementation and thesubstantially higher computational cost when solving linearsystems.  more » « less
Award ID(s):
1925595 1821210 1835673
NSF-PAR ID:
10359238
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Solid Earth
Volume:
13
Issue:
1
ISSN:
1869-9529
Page Range / eLocation ID:
229 to 249
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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