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.

翻译：在最小二乘有限元框架下研究非线性海冰问题。分析了同时逼近应力张量与速度的相应变分形式。特别地，最小二乘泛函在适当解空间中具有强制性与连续性，从而证明了问题的适定性。由于该方法不要求有限元空间之间存在相容性条件，此变分形式允许对应力与速度的逼近采用相同逼近阶的分片多项式空间。采用牛顿型迭代法对问题进行线性化，并通过数值实验验证理论结果。