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In this paper, we investigate the spectral properties of condensed matrices in mixed hybrid discretizations of the Neumann boundary value problem for the Poisson equation on distorted meshes. We also consider a new approach to the construction of spectrally equivalent preconditioners to the condensed matrices. The proposed preconditioners are the stiffness matrices of the standard piecewise linear finite element method on triangular/tetrahedral meshes. Generalization to the Dirichlet and mixed boundary conditions as well as to variable coefficients is basically straightforward.

Spectrally equivalent preconditioners for mixed hybrid discretizations of diffusion equations on distorted meshes