*node*- a vertex in the mesh
*element*- a polygonal or polyhedral piece in the mesh; most often a triangle, quadrilateral, tetrahedron, or hexahedron (brick)
*triangulation*- given a set of points, connect them into a mesh of triangles
*mesh generation*- given a (typically 2-D or 3-D) domain, generate nodes and triangulate them to create a mesh
*anisotropic*- not the same in all directions
*anisotropic mesh generation*- uses stretched elements; desired edge length is a function of orientation; e.g. doesn't strive for equilateral triangles
*graded mesh generation*- uses elements that vary in size as a function of position
*structured mesh*- all elements and nodes have the same topology (i.e. same number of neighbors)
*unstructured mesh*- elements and nodes can have different topology; e.g. an arbitrary triangular subdivision
*adaptive meshing*- iteratively regenerate mesh and solve FEM problem, hopefully improving the mesh and the accuracy of the solution on each iteration

Paul Heckbert