A mimetic iterative scheme for solving biharmonic equations

A new mimetic iterative scheme for solving general biharmonic equations under Robin’s conditions is presented. This approach combines recently developed mimetic techniques for partial differential equations (PDEs) with an efficient iterative scheme based on a global conjugate gradient and a local preconditioned biconjugate gradient methods. The elegant matrix formulation of mimetic methods allows us to present an original convergence analysis of the proposed scheme. Numerical experiments provide strong evidences of the advantages of the novel approach.