Conclusion
Metric and mesh: Definition and theoretical basics

In this article, we introduced the notion of generalized metric. This concept has enabled us firstly to define the metric of a simplicial geometric element and secondly to propose a rigorous definition for a mesh. A mesh is then seen as a Riemannian space whose metrics characterize the elements of the mesh. As this definition is universal, it encompasses the notions of mesh, mesh adaptation and remeshing. A few classical examples of plane, surface and volume meshes are given to illustrate the concept.

In the following, we focus on mesh adaptation and remeshing problems