The FELIM model is being developed in the scope of the Second generation Louvain-la-Neuve Ice-ocean Model (SLIM). This sea-ice model has representations of both dynamic and thermodynamic sea-ice processes and includes viscous–plastic rheology along with a complete parameterization of the atmospheric fluxes. The dynamical equations are written in a local element-based coordinate system solving the problem of the singularity at the poles arising when the mesh is based on a geographical coordinate system. The numerical resolution of this set of equations involves the standard Galerkin formulation and a Newton iterative procedure. The climatological sea-ice drifts, thicknesses and concentrations computed by the model compare qualitatively well with the observations. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands such as the Canadian Arctic Archipelago (CAA). We have shown that the local and short-term influences of the ice exchanges through the CAA are non-negligible. In particular, whether some straits are open or closed in the numerical experiment influences directly the numerical solution in the vicinity of those straits. Moreover, on average, the sea-ice volume in the CAA represents 10% of the total sea-ice volume in our model and a non-negligible freshwater volume is exported to Baffin Bay and the Labrador Sea. Another ongoing study is the development of a Lagrangian adaptive sea-ice model allowing the computational grid to move with the ice drift. In order to maintain a good quality of the mesh, the mesh has to be adapted during the simulation, involving particular mesh adaptation techniques. This Lagrangian version of the model has several interesting applications, such as the dynamical mesh refinement along any region of interest (e.g. the ice edge), buoys tracking, or the inclusion of material properties in the rheology.