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.
翻译:我们在三角网格上呈现了稳定的海冰动态分解,可以直截了当地与三角网格上的海洋模型和Arakawa C型惊人的三角网格相连接。这个方法基于一个不兼容的有限元素框架,即Crouzix-Raviart的限定元素。由于粘结-塑料和弹性-血管-塑料压力的分解与Crouzix-Raviart的限定元素的分解在速度场中产生振荡,我们引入了一种以边缘为基础的稳定。为了表明稳定的Crouzix-Raviart的近似在质量上与持续海冰方方形的解决方案一致,我们得出了1美元的估计数。在一项数字分析中,我们表明稳定对于实现海冰速度场的稳定近似至关重要。