A conforming mesh is a mesh in which the intersection of any two distinct cells is empty or is a complete face of both cells. The cells therefore meet face-to-face, without partial overlaps or hanging nodes. For example, a vertex of one triangle cannot lie in the relative interior of an edge of an adjacent triangle unless the edge is subdivided so that the vertex belongs to both cells (Bern and Plassmann 2000).
A conforming mesh whose cells are all simplices, together with all the faces of those cells, forms a geometric simplicial complex. In the finite element method, conformity allows degrees of freedom on shared cell faces to be identified consistently when constructing continuous finite element spaces (Brenner and Scott 1994).
