Stiffness matrix
In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix is a matrix that represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. == The stiffness matrix for the Poisson problem == For simplicity, we will first consider the Poisson problem − ∇ 2 u = f {\displaystyle -\nabla ^{2}u=f} on some domain Ω, subject to the boundary condition u = 0 on the boundary of Ω. To discretize this equation by the finite element method, one chooses a set of basis functions {φ1, …, φn} defined on Ω which also vanish on the boundary.