Vector Interpolation On Natural Element Method: Mesh Sensitivity Analysis

In a previous work a vector interpolation scheme based on the Natural Element Method (NEM) was introduced. For this, the standard NEM shape functions associated to the nodes of a mesh composed of arbitrarily shaped polygons were used to construct the vector functions linked to the edges of the polygonal elements. The scheme, which can be seen as an edge-based Finite Element Method extension to polygonal meshes, potentially simplifies the mesh generation and yields higher order approximations. Here, the sensitivity of this approach to the mesh regularity is examined.