Mesh: representation of a domain by a set of cells and nodes. Cells and nodes are named entities. There is no notion of edges or faces.
The dimension of a mesh is characterized by two parameters: the size of the space wherein the mesh is immersed, and the (maximum) size of the mesh cells. Examples: 3D surface mesh (3D space, 2D cells), 3D mesh (3D space, 3D cells), curved 2D mesh (2D space, 1D cells)...

Field: physical quantity whose value varies in space and time. Represented by a result vector V obtained from one or more tables of values A, at any point of space covered by a mesh and in time defined by its temporal resolution. The size of V is called the number of components (equal to the number of components of A). A P1 field is a field where values are stored at node level, a P0 field is a field where values are stored at cell level.
Intensive field: represents intensive physical data (i.e. which do not depend on the amount of material). Examples: density, power density, temperature, pressure.
Extensive field: represents extensive physical data (i.e. proportional to the size of the physical system represented). Examples: mass, volume, time, power.
The mesh support identifies both the mesh and the entity on which it is defined.

Family: partition of a mesh (nodes and cells with the same identifier). Every node or cell can only belong to one family, i.e. the intersection of two families is zero.
Group: a set of families; two groups may share elements.
Profile: subset of the entities of a mesh.
Field profile: indicates on which mesh entities field values are located (a field being defined on a part of a mesh).

The connectivity of a mesh represents the kind of connections between its vertices.
The nodal connectivity is the description of a mesh entity by the ordered list of its nodes.
The descending connectivity is the description of N-dimensional mesh entities by the ordered list of (N-1)-dimensional geometrical entities.

Intersector: algorithm that calculates the intersection of two cells from their position and geometry.
Maximum principle: a property of solutions to certain partial differential equations, of the elliptic and parabolic types; it says that the maximum of a function in a domain is to be found on the boundary of that domain.
Conservativity: preservation of conservation laws governing physical quantities during their discretization or their interpolation.
Projection: modification (by interpolation) of the entity on which a field is defined. The projection is called conservative if the interpolation uses intersection detection. The projection is said not conservative if the interpolation localizes a cloud of points in a mesh.
The Gauss integration points are the geometrical points where the numerical integration of a given quantity is performed. Precise location of these nodes and a sufficient number (related to the approximation order of the integration term) allow for an exact integration in the case of polynomial functions integration.
Kriging: a linear estimation method guaranteeing minimum variance. The estimate at a given point P is obtained locally from the point values on a neighbourhood of P.
Code coupling: run of two numerical codes (or two instances of the same code) in such a way that information is passed from one instance to the other.