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Abstract. Time-dependent simulations of ice sheets require two equations to be solved:the mass transport equation, derived from the conservation of mass, and thestress balance equation, derived from the conservation of momentum. The masstransport equation controls the advection of ice from the interior of the icesheet towards its periphery, thereby changing its geometry. Because it isbased on an advection equation, a stabilization scheme needs to beemployed when solved using the finite-element method. Several stabilizationschemes exist in the finite-element method framework, but their respectiveaccuracy and robustness have not yet been systematically assessed forglaciological applications. Here, we compare classical schemes used in thecontext of the finite-element method: (i) artificial diffusion, (ii)streamline upwinding, (iii) streamline upwind Petrov–Galerkin, (iv)discontinuous Galerkin, and (v) flux-corrected transport. We also look at thestress balance equation, which is responsible for computing the ice velocitythat “advects” the ice downstream. To improve the velocity computationaccuracy, the ice-sheet modeling community employs several sub-elementparameterizations of physical processes at the grounding line, the point wherethe grounded ice starts to float onto the ocean. Here, we introduce a newsub-element parameterization for the driving stress, the force that drives theice-sheet flow. We analyze the response of each stabilization scheme byrunning transient simulations forced by ice-shelf basal melt. The simulationsare based on an idealized ice-sheet geometry for which there is no influenceof bedrock topography. We also perform transient simulations of the AmundsenSea Embayment, West Antarctica, where real bedrock and surface elevations areemployed. In both idealized and real ice-sheet experiments, stabilizationschemes based on artificial diffusion lead systematically to a bias towardsmore mass loss in comparison to the other schemes and therefore should beavoided or employed with a sufficiently high mesh resolution in the vicinityof the grounding line. We also run diagnostic simulations to assess theaccuracy of the driving stress parameterization, which, in combination with anadequate parameterization for basal stress, provides improved numericalconvergence in ice speed computations and more accurate results.