2006•Numerical Methods for Partial Differential EquationsRequires access

Superconvergence of finite volume element method for a nonlinear elliptic problem

Chunjia Bi

Abstract

Abstract In this article, we consider the finite volume element method for the second‐order nonlinear elliptic problem and obtain the H1 and W1,∞ superconvergence estimates between the solution of the finite volume element method and that of the finite element method, which reveal that the finite volume element method is in close relationship with the finite element method. With these superconvergence estimates, we establish the Lp and W1,p (2 < p ≤ ∞) error estimates for the finite volume element method for the second‐order nonlinear elliptic problem. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007

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Key concepts: Superconvergence, Finite element method, Mathematics, Mixed finite element method, Finite volume method, Nonlinear system, Extended finite element method, Finite volume method for one-dimensional steady state diffusion