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 analyzed. Under additional smoothness assumptions, the least-squares functional is equivalent to the norm in a neighbourhood of the solution. As the method does not require a compatibility condition between the finite element spaces, 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 linearise the problem and numerical tests are provided to illustrate the theory.

中文翻译：

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海冰运动模拟的最小二乘有限元法


在最小二乘有限元设置中考虑非线性海冰问题。分析了同时逼近应力张量和速度的相应变分公式。在额外的平滑度假设下，最小二乘函数相当于解的邻域中的范数。由于该方法不需要有限元空间之间的兼容性条件，因此该公式允许对应力和速度近似使用相同近似阶数的分段多项式空间。使用牛顿型迭代方法来线性化问题，并提供数值测试来说明该理论。