Introduction to Multigrid Methods

0 = x0 < x1 < . . . xN < xN+1 = 1, xj = jh, j = 0 : N + 1, where h = 1/(N + 1) is the length of each subinterval. Let φi be the hat basis function at xi for i = 0 : N + 1. For a linear finite element function v = ∑N i=1 viφi, we denote by v = (v1, . . . , vN ) the vector formed by the coefficients. The boundary nodes (i = 0, N + 1) are excluded due to the homogenous Dirichlet boundary condition. We consider the algebraic system of a scaling of finite element or finite difference discretization