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The viscous‐plastic sea ice model based on [2] describes the motion of sea ice for scales of several thousand kilometers. The numerical model for the simulation of sea ice circulation and evolution over a seasonal cycle includes the consideration of the sea ice thickness and sea ice concentration. Transient advection equations describe the physical behavior of both thickness and concentration with the velocity of the sea ice as the coupling field. Recent research on a finite element implementation of the sea ice model is devoted to formulations based on the (mixed) Galerkin variational approach, compare to [1] and [6] for instance. Here, particular treatments are necessary regarding the stabilization of the complex numerical scheme, especially for the first‐order advection equation. It is therefore suggested to utilize the mixed least‐squares finite element method (LSFEM), which is well established in the branch of, e.g., fluid mechanics. A significant advantage of the method is its applicability to first‐order systems. Thus, this method results in stable and robust formulations also for not self‐adjoint operators like the tracer equations. Moreover, in [7], the authors provide a promising higher‐order time integration scheme for transient advection equations denoted as Taylor‐least‐squares scheme, which is investigated in this article. The presented least‐squares finite element formulation is based on the unsteady sea ice equations including two tracer equations of transient advection type. The numerical problem of a Box test case is investigated.

In the framework of solving elastodynamic problems using a least-squares mixed finite element method (LSFEM) the implementation of a stress-velocity formulation for small strains is introduced and discussed in the present contribution. The element formulation is based on a first-order div − grad system, with the balance equation of momentum and the constitutive law as the governing equations. Application of the L2-norm to the two residuals leads to a functional depending on stresses and velocities. Different time discretization schemes are considered, a scalar weighting is introduced and chosen in dependency of the different time discretization methods. In a numerical example the influence of the time integration method, the chosen time step width and the related weighing factor are investigated for a two-dimensional problem.

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