Polynomial preserving recovery for the finite volume element methods under simplex meshes

Abstract

The recovered gradient, using the polynomial preserving recovery (PPR), is constructed for the finite volume element method (FVEM) under simplex meshes. Regarding the main results of this paper, there are two aspects. Firstly, we investigate the supercloseness property of the FVEM, specifically examining the quadratic FVEM under tetrahedral meshes. Secondly, we present several guidelines for selecting computing nodes such that the least-squares fitting procedure of the PPR admits a unique solution. Numerical experiments demonstrate that the recovered gradient by the PPR exhibits superconvergence.