Boundary preconditioners for mixed finite-element discretizations of fourth-order elliptic problems

Abstract We extend the preconditioning approach of Glowinski and Pironneau, and of Peisker to the case of mixed finite element general fourth-order elliptic problems. We show thatH−1/2-preconditioning on the boundary leads to mesh-independent performance of iterative solvers of Krylov subspace type. In particular, we show that the field of values of the boundary Schur complement preconditioned by a discrete H−1/2 boundary norm is bounded independently of the discretization.

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