Representing a Field Quantity in the Finite Element Method (FEM)

A FEM solver stores the value of a field quantity (such as electric potential) at each mesh node of a triangular or tetrahedral element. Inside each element, the field is interpolated from the values stored at the mesh nodes using local finite element basis functions.

When field quantities are represented in this way, it is possible to transform Maxwell 's partial differential equations into a sparse matrix of linear algebraic equations ("sparse" because it has many zero-valued entries) that can be solved using traditional direct or iterative numerical methods.