Stable splitting of polyharmonic operators by generalized Stokes systems

Abstract

A stable splitting of 2<em>m</em>-th order elliptic partial differential equations into 2(<em>m</em>−1) problems of Poisson type and one generalized Stokes problem is established for any space dimension <em>d</em> ≥ 2 and any integer <em>m</em> ≥ 1. This allows a numerical approximation with standard finite elements that are suited for the Poisson equation and the Stokes system, respectively. For some fourth- and sixth-order problems in two and three space dimensions, precise finite element formulations along with a priori error estimates and numerical experiments are presented.