Nested tetrahedral grids and strengthened CBS inequality

The paper deals with nested two-level decompositions of 3D domains into tetrahedra and the corresponding spaces of continuous piecewise linear finite element (FE) functions. The decomposition of the fine grid FE space into the coarse grid FE space and its complement can be used for the construction of various multi-level iterative methods and preconditioners, which are efficient for the finite element solution of boundary value problems (BVP) in the considered domains. The constant in the strengthened Cauchy-Bunyakowski-Schwarz (C.B.S.) inequality for the coarse grid FE space and its complement determines the efficiency of these multi-level methods and preconditioners. From this reason, this constant is investigated in this paper for the case of BVP with anisotropic Laplacian or elasticity operators. Special emphasis is given on getting universal estimates of the C.B.S. inequality constant, which are valid for all kinds of physical or discretization anisotropy. Copyright (C) 2003 John Wiley Sons, Ltd.