ABSTRACT

The motion of sea ice in large scales of several thousand kilometers is modeled by the viscous-plastic (VP) sea ice rheology. The sea ice motion model is based on the findings of Hibler III (1979), who introduced a numerical model for the simulation of sea ice circulation and thickness evolution over a seasonal cycle. The velocity and stress fields, as well as the sea ice thickness and sea ice concentration, are included in the model. Recent research on a finite element implementation of the model is devoted to formulations based on the (mixed) Galerkin variational approach. Here, special treatments are necessary regarding the stabilization of the numerical complex scheme. It is therefore suggested to utilize a mixed least-squares formulation to overcome possible numerical drawbacks. The least-squares finite element method is well established, especially in the branch of fluid mechanics, see e.g. Jiang (1998), Cai et al. (2004) and Bochev & Gunzburger (2009). A significant advantage of the method is its applicability to first-order systems, such that it results in stable and robust formulations also for not self-adjoint operators like in the Navier-Stokes equations.

The presented least-squares finite element formulations are based on the instationary sea ice equations including two tracer equations of transient convection type. Therefore, the mixed least-squares approach includes four primary fields, which are the stress tensor σ , the velocity field ν and two scalar tracers A ice and H ice . Different time-integrators are investigated regarding accuracy and stability with a particular focus on the treatment of the tracer equations. The investigation of the formulation with the help of a boundary value problem is provided.