Flexible representation of computational meshes

A new representation of computational meshes is proposed in terms of a covering relation defined by discrete topological objects we call sieves. Fields over a mesh are handled locally by using the notion of refinement, dual to covering, and are later reassembled. In this approach fields are modeled by sections of a fiber bundle over a sieve. This approach cleanly separates the topology of the mesh from its geometry and other value-storage mechanisms. With these abstractions, finite element calculations are expressed using algorithms that are independent of mesh dimension, global topology, element shapes, and the finite element itself. Extensions and other applications are discussed