Stable splitting of polyharmonic operators by generalized Stokes systems

A stable splitting of 2 m 2m -th order elliptic partial differential equations into 2 ( m − 1 ) 2(m-1) problems of Poisson type and one generalized Stokes problem is established for any space dimension d ≥ 2 d≥ 2 and any integer m ≥ 1 m≥ 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.