Sea-ice dynamics on triangular grids

• Main Authors: Mehlmann, Carolin, Korn, Peter
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: arXiv 2020
• Subjects: Numerical Analysis math.NA; FOS Mathematics; Sea ice
• Online Access: https://dx.doi.org/10.48550/arxiv.2006.00547; https://arxiv.org/abs/2006.00547

We present a stable discretization of sea-ice dynamics on triangular grids that can straightforwardly be coupled to an ocean model on a triangular grid with Arakawa C-type staggering. The approach is based on a nonconforming finite element framework, namely the Crouzeix-Raviart finite element. As the discretization of the viscous-plastic and elastic-viscous-plastic stress tensor with the Crouzeix-Raviart finite element produces oscillations in the velocity field, we introduce an edge-based stabilization. To show that the stabilized Crouzeix-Raviart approximation is qualitative consistent with the solution of the continuous sea-ice equations, we derive a $H^1$-estimate. In a numerical analysis we show that the stabilization is fundamental to achieve stable approximation of the sea-ice velocity field.