Element agglomeration coarse Raviart–Thomas spaces with improved approximation properties

Abstract

SUMMARY We propose a new technique based on element agglomeration for constructing coarse subspaces of the lowest‐order tetrahedral Raviart–Thomas finite element space. The coarse spaces are spanned by local basis functions associated with each coarse face (i.e., with an interface between two agglomerated elements). Each such face is associated with up to four coarse basis functions. The support of these functions extends into the neighboring agglomerated elements, and the construction of these functions involves solution of certain local mixed finite element problem on each neighboring agglomerated element. In contrast to some previous work, the thus constructed coarse subspace exhibits improved approximation properties because under certain conditions, it locally contains (i.e., interpolates exactly) all vector constants. Our construction is general; in particular, we do not assume that the coarse faces are planar. Possible applications of the coarse Raviart–Thomas spaces are in constructing multigrid methods for the H ( div ) bilinear forms and (on the basis of the approximation properties of these spaces) in upscaling of mixed formulation of diffusion problems. Copyright © 2012 John Wiley & Sons, Ltd.