Interpolation error with the PCD Method on 3D-Composite Grid

Abstract

In this article, we present the interpolation error (the discretization error) with the PCD method in 3D order on composite grid. As in 2D order, for all function/distribution that is locally $H^2$, the discretization error (interpolation error) has an $O(h)$-convergence rate independently of the presence or not of the local mesh refinement. Here, we prove that the present method has the same $O(h)$-convergence rate on 3D-composite grid. In addition, its properties still valid in 3D order, namely the discrete versions of the Friedrichs inequalities and the trace inequality.