Two-grid finite element method and its a posteriori error estimates for a nonmonotone quasilinear elliptic problem under minimal regularity of data

Chunjia Bi, Cheng Wang, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

Abstract

In this paper, we propose and analyze a two-grid finite element method for a class of quasilinear elliptic problems under minimal regularity of data in a bounded convex polygonal Ω⊂R 2, which can be thought of as a type of linearization of the nonlinear system using a solution from a coarse finite element space. With this technique, solving a quasilinear elliptic problem on the fine finite element space is reduced into solving a linear problem on the fine finite element space and solving the quasilinear elliptic problem on a coarse space. Convergence estimates in the H 1-norm are derived to justify the efficiency of the proposed two-grid algorithm. Moreover, we propose a natural and computationally efficient residual-based a posteriori error estimator of the two-grid finite element method for this nonmonotone quasilinear elliptic problem and derive the global upper and lower bounds on the error in the H 1-norm. Numerical experiments are provided to confirm our theoretical findings.

Original languageEnglish
Pages (from-to)98-112
Number of pages15
JournalComputers and Mathematics with Applications
Volume76
Issue number1
DOIs
Publication statusPublished - 1 Jul 2018

Keywords

  • A posteriori error estimates
  • Quasilinear elliptic problems
  • Two-grid finite element method

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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