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

作者：Zhang Tie^*; Sheng Ying

来源：Numerical Methods for Partial Differential Equations, 2014, 30(4): 1152-1168.

DOI：10.1002/num.21862

• convection-diffusion equation
• superconvergence
• bilinear finite volume element
• gradient recovery

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.

• 出版日期2014-7
• 单位东北大学