On a least‐squares finite element formulation for sea ice dynamics

Abstract

AbstractIn this contribution a mixed least‐squares finite element method (LSFEM) for the modeling of sea ice motion including a viscous‐plastic (VP) sea ice rheology is investigated. The simulation of sea ice motion goes back to the findings in Hibler III [4], where a numerical model for the simulation of sea ice circulation and thickness evolution over a seasonal cycle is introduced. Both the ice thickness and ice concentration distribution are explicitly described on the basis of evolution equations. Recent research in this field is devoted to finite element formulations based on the Galerkin variational approach. Here, special focus lies on the stabilization of the numerically complex scheme. It is therefore desirable to establish a least‐squares formulation to overcome possible numerical drawbacks. The least‐squares variational approach is well established in finite element formulations in the branch of fluid mechanics, see [2], [3] and [6], for instance. A great 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, for instance. A box test case, see [7], is investigated for the least‐squares formulation.