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Title: Finite volume element method for monotone nonlinear elliptic problems
Authors: Bi, C
Lin, Y 
Yang, M
Keywords: A posteriori
A priori
Error estimates
Finite volume element method
Monotone nonlinear elliptic problems
Issue Date: 2013
Publisher: Wiley-Blackwell
Source: Numerical Methods for Partial Differential Equations, 2013, v. 29, no. 4, p. 1097-1120 How to cite?
Journal: Numerical Methods for Partial Differential Equations 
Abstract: In this article, we consider the finite volume element method for the monotone nonlinear second-order elliptic boundary value problems. With the assumptions which guarantee that the corresponding operator is strongly monotone and Lipschitz-continuous, and with the minimal regularity assumption on the exact solution, that is, u∈H1(Ω), we show that the finite volume element method has a unique solution, and the finite volume element approximation is uniformly convergent with respect to the H1 -norm. If u∈H1+ε(Ω),0 < ε ≤ 1, we develop the optimal convergence rate O(hε) in the H1 -norm. Moreover, we propose a natural and computationally easy residual-based H1 -norm a posteriori error estimator and establish the global upper bound and local lower bounds on the error.
ISSN: 0749-159X
DOI: 10.1002/num.21747
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