LOCAL CHEBYSHEV PROJECTION–INTERPOLATION OPERATOR AND APPLICATION TO THE h–p VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS

Abstract

In this paper, we construct local Chebyshev projection–interpolation operators for tetrahedral and hexahedral elements in three dimensions based on the framework of the Jacobi-weighted Sobolev and Besov spaces. A simple assembly of the local Chebyshev projection–interpolations ΠΩj u on all the elements Ωj, 1 ≤ j ≤ J, leads to a globally continuous and piecewise polynomial which possesses the best approximation properties locally and globally. By applying the local Chebyshev projection–interpolation operators to the h–p version of the finite element method with general tetrahedral or hexahedral meshes for second-order elliptic problems in three dimensions, we establish the convergence rate for problems with homogeneous Dirichlet boundary conditions and the solution [Formula: see text], and for problems with nonhomogeneous Dirichlet boundary conditions and the solution [Formula: see text].