On the choice of finite element for applications in geodynamics

Abstract. Geodynamical simulations over the past decades have widely been built on quadrilateral and hexahedral finite elements. For discretization of key Stokes equation describing slow, viscous flow, most codes use either unstable Q1×P0 element, a stabilized version equal-order Q1×Q1 or more recently stable Taylor–Hood element with continuous (Q2×Q1) discontinuous (Q2×P-1) pressure. However, it is not clear which these choices actually best at accurately simulating “typical” geodynamic situations. Herein, we provide systematic comparison all elements for first time. We series benchmarks that illuminate different aspects features consider typical mantle convection geodynamical simulations. will show in particular has great difficulty producing accurate solutions buoyancy-driven flows – dominant forcing flow too inaccurate practice. As consequence, believe Q2×Q1 Q2×P-1 robust reliable choice simulations, despite greater complexity their implementation substantially higher computational cost when solving linear systems.