Superconvergence and gradient recovery for a finite volume element method for solving convection-diffusion equations

We study the superconvergence of the finite volume element (FVE) method for solving convection-diffusion equations using bilinear trial functions. We first establish a superclose weak estimate for the bilinear form of FVE method. Based on this estimate, we obtain the H-1-superconvergence result: ||pi hu-uh||1=O(h2). Then, we present a gradient recovery formula and prove that the recovery gradient possesses the O(h2)-order superconvergence. Moreover, an asymptotically exact a posteriori error estimate is also given for the gradient error of FVE solution.Copyright (c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1152-1168, 2014