Least-Squares finite element method for the simulation of sea-ice motion ...

• Main Authors: Bertrand, Fleurianne, Schneider, Henrik
• Format: Report
• Language: unknown
• Published: arXiv 2023
• Subjects: Numerical Analysis math.NA; FOS Mathematics; Sea ice
• Online Access: https://dx.doi.org/10.48550/arxiv.2305.11635; https://arxiv.org/abs/2305.11635

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. ...