Collocation and full multigrid methods (Q1098596)

A linear elliptic boundary value problem L \(u=f\) on \(\Omega\) with homogeneous boundary conditions on \(\partial \Omega\) is considered. Here L denotes a linear elliptic differential operator of order 2m and the solution of this problem is seeked in some space U \((=C^{2m}(\Omega)\) or \(H^{2m,p}(\Omega))\). In order to find an approximation for the solution a full multigrid method is applied to the above problem discretized by the collocation method. For this purpose the collocation method and the structure of the full multigrid method are described and some theoretical results and an example are given.