Finite element three-dimensional Stokes ice sheet dynamics model with enhanced local mass conservation

Abstract

Parallel finite element nonlinear Stokes models have been successfully used for three-dimensional ice-sheet and glacier simulations due to their accuracy and efficiency, and their capability for easily handling highly irregular domains and different types of boundary conditions. In particular, the well-known Taylor–Hood element pair (continuous piecewise quadratic elements for velocity and continuous piecewise linear elements for pressure) results in highly accuracy velocity and pressure approximations. However, the Taylor–Hood element suffers from poor mass conservation which can lead to significant numerical mass balance errors for long-time simulations. In this paper, we develop and investigate a new finite element Stokes ice sheet dynamics model that enforces local element-wise mass conservation by enriching the pressure finite element space by adding the discontinuous piecewise constant pressure space to the Taylor–Hood pressure space. Through various numerical tests based on manufactured solutions, benchmark test problems, and the realistic Greenland ice-sheet, we demonstrate that, for ice-sheet modeling, the enriched Taylor–Hood finite element model remains highly accurate and efficient, and is physically more reliable and robust compared to the classic Taylor–Hood finite element model.