Finite volume element method for monotone nonlinear elliptic problems

Chunjia Bi, Yanping Lin, Min Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1097-1120
Number of pages24
JournalNumerical Methods for Partial Differential Equations
Volume29
Issue number4
DOIs
Publication statusPublished - 1 Jul 2013

Keywords

  • a posteriori
  • a priori
  • error estimates
  • finite volume element method
  • monotone nonlinear elliptic problems

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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