The mesh generators discretize the domains (intervals) into smaller intervals (or mesh elements). The endpoints of the mesh elements are called mesh vertices.

The boundaries (or vertices) defined in the geometry are represented in the mesh by boundary elements (or vertex elements).

The mesh generators discretize the domains into triangular or quadrilateral mesh elements. If the boundary is curved, these elements represent an approximation of the original geometry. The sides of the triangles and quadrilaterals are called mesh edges, and their corners are mesh vertices. A mesh edge must not contain mesh vertices in its interior.

The boundaries defined in the geometry are discretized (approximately) into mesh edges, referred to as boundary elements (or edge elements), which must conform with the mesh elements of the adjacent domains.

The mesh generators discretize the domains into tetrahedral, hexahedral, prism, or pyramid mesh elements whose faces, edges, and corners are called mesh faces, mesh edges, and mesh vertices, respectively.

Meshes generated in the COMSOL Multiphysics software are conforming with a geometric model. In a conforming mesh, the intersection between any two elements in the mesh is defined by subelements (mesh face, mesh edge, or mesh vertex). Each mesh element belongs to exactly one geometric entity. For a mesh conforming with a geometry, each geometric entity is either unmeshed or fully meshed.

A mesh of assembly type can either be conforming with a geometry where the Form an Assembly finalization action has been used, or it defines its own geometric model. Regardless of its origin, an assembly type of mesh defines several disconnected components with duplicated boundaries, edges, and points where the components are touching. The boundary meshes at touching surfaces between two parts do not need to define geometrically matching mesh vertices and elements. The image to the left in Figure 8-1 shows a nonmatching assembly mesh with two disconnected components. The exploded view to the right shows that the two components are indeed disconnected. The mesh contains 21 mesh vertices and 20 triangle elements, 2 domains (indicated by yellow and green colors), 8 edges, and 8 points.

To connect the physics in disconnected components, set up Identity pairs and add pair boundary conditions in the physics interfaces. See About Identity and Contact Pairs for more information.

When importing nonconforming mesh data, the Import operation will typically create edge and boundary elements of the mesh edges and boundaries corresponding to each nonconformity in the mesh, since these mesh edges and boundaries are typically only adjacent to one element each. In Figure 8-2, the image to the left shows the result after importing nonconforming mesh data, with so-called hanging nodes. The mesh contains 18 mesh vertices and 20 triangle elements, compared to the assembly mesh in Figure 8-1 which contains 21 mesh vertices. The resulting domains are connected in points 3, 4, and 6 with slit-like holes between the domains, as seen in the exploded view in the right image. Note that the mesh gets 2 domains (indicated by color), 10 edges, and 7 points.

Similarly, import of nonconforming mesh data containing a 3D volume mesh typically result in many duplicated boundaries (faces) with slit-like pocket holes. Such a mesh is not well suited for simulations in COMSOL Multiphysics. Use the mesh operations Union or Merge Entities to merge the nearby faces defining the interface between two parts and to create a mesh that is connected across the interface, as seen in Figure 8-3.

Import of nonconforming mesh data with so called hanging edges results in an error. A hanging edge appears when two triangles (yellow in Figure 8-4) coincide with a quad element (blue) with which they share mesh vertices.