  A nonlinear sea-ice problem is considered in a least-squares finite element
setting. The corresponding variational formulation approximating simultaneously
the stress tensor and the velocity is analysed. In particular, the
least-squares functional is coercive and continuous in an appropriate solution
space and this proves the well-posedness of the problem. As the method does not
require a compatibility condition between the finite element space, the
formulation allows the use of piecewise polynomial spaces of the same
approximation order for both the stress and the velocity approximations. A
Newton-type iterative method is used to linearize the problem and numerical
tests are provided to illustrate the theory.
