Stable splitting of polyharmonic operators by generalized Stokes systems

A stable splitting of 2m-th order elliptic partial differential equations into 2(m− 1) problems of Poisson type and one generalized Stokes problem is established for any space dimension d ≥ 2 and any integer 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 fourthand sixth-order problems in two and three space dimensions, precise finite element formulations along with a priori error estimates and numerical experiments are presented.

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