Finite Element Method

The following are some of the characteristics of Finite Element Method (FEM):

FEM Discretization

The starting point of the FEM is the subdivision of the domain into small subdomains called elements. An element is described by its vertices and one point on each edge. These points are called the nodes. The FEM mesh is constituted by the nodes and the elements.

Continuous Mesh

The mesh has to be continuous. If two elements touch, then the set of the common points has to be an edge or a vertex of each of the elements.

Structured & Unstructured Meshes

Structured meshes are characterized by regular connectivity. All interior chord nodes (on the extremities) of a structured mesh are connected to the same number of element edges. Unstructured meshes allow any number of elements to meet at a single chord node.

Mesh Requirements

FEM has certain requirements on a mesh:

• The mesh must be valid (no holes, self-intersections, or faces joined at two or more edges).
• The mesh must conform to the boundary of the domain.
• The density of the mesh must be controllable, to allow trade-off between accuracy and time.

Mesh Density

Choosing the correct mesh density required to solve a problem is an important factor. If the mesh is too coarse, then the element will not allow a correct solution to be obtained. Alternatively, if the mesh is too fine, the cost of analysis in computing time can be out of proportion to the results obtained.

A Good Mesh

A good or appropriate mesh is one that enables accurate resolution of the underlying physical phenomena, yet is coarse enough to allow a fast solution time.