When discretizing the analytical problem the chosen grid type must be accounted for. Different numerical methods require special kinds of grids and the discretization process depends on the grid type, too.
One way to classify grids is by their basic grid elements. Grids with only one element class have to be distinguished from grids with multiple element classes. It can often be an advantage to allow differently shaped elements, since the use of different element types may result in grids that are more flexible. The boundary approximation of these elements can sometimes be better and the total number of grid elements is usually reduced. However, those mixed element grids are often not easy to handle with regard to both grid generation as well as numerical discretization. The numerical discretization method must be applicable for all types of elements that are used in the grid, which limits the set of usable element types and reduces the flexibility of this method. Therefore, in most simulators only mixed element grids with some basic element types, such as rectangles and triangles or tetrahedrons and cuboids, are implemented.
Within this work, we will only consider simple element grids, and discriminate between triangular shaped elements, which are triangles in two dimensions and tetrahedrons for three dimensions, and rectangle shaped elements, rectangles for two dimensions and cuboids for three dimensions. The second kind of grids are usually known as ortho-product or ortho grids.