Sea-ice dynamics on triangular grids

TL;DR

This paper introduces a stable, finite element discretization method for simulating sea-ice dynamics on triangular grids, incorporating stabilization techniques to ensure accurate and stable velocity field approximations.

Contribution

It presents a novel nonconforming finite element approach using Crouzeix-Raviart elements with edge-based stabilization for sea-ice modeling on triangular grids.

Findings

The stabilized method produces oscillation-free velocity fields.

The approach is consistent with continuous sea-ice equations.

Numerical results confirm the method's stability and accuracy.

Abstract

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.