Stiffness matrix

Summary

The stiffness matrix is the matrix of the linear system that the finite element method produces from the bilinear form of a boundary value problem. Its entries are the values of the form on pairs of basis functions. Because finite element basis functions have small supports, the matrix is sparse. For symmetric coercive problems such as the Poisson equation it is symmetric and positive definite. The name comes from structural mechanics, where the matrix links the displacements of the nodes with the forces on them. See the definition.