Multigrid methods with Powell-Sabin splines

Abstract

This paper presents a multigrid algorithm for the solution of the linear systems that arise from a finite-element discretization of second-order elliptic partial differential equations with Powell-Sabin (PS) splines. We show that the method yields a uniform convergence in the l 2 -norm which is independent of the mesh size. We also briefly consider the use of PS splines for the fourth-order biharmonic problem.