Error estimates for finite volume element methods for general second-order elliptic problems

✍ Scribed by Haijun Wu; Ronghua Li

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 129 KB
• Volume: 19
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.10068

✦ Synopsis

Abstract

We treat the finite volume element method (FVE) for solving general second order elliptic problems as a perturbation of the linear finite element method (FEM), and obtain the optimal H^1^ error estimate, H^1^ superconvergence and L^p^ (1 < p ≤ ∞) error estimates between the solution of the FVE and that of the FEM. In particular, the superconvergence result does not require any extra assumptions on the mesh except quasi‐uniform. Thus the error estimates of the FVE can be derived by the standard error estimates of the FEM. Moreover we consider the effects of numerical integration and prove that the use of barycenter quadrature rule does not decrease the convergence orders of the FVE. The results of this article reveal that the FVE is in close relationship with the FEM. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 693–708, 2003.