Pointwise Error Estimates and Two-Grid Algorithms of Discontinuous Galerkin Method for Strongly Nonlinear Elliptic Problems

Chunjia Bi, Cheng Wang, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

Abstract

In this paper, we consider the discontinuous Galerkin finite element method for the strongly nonlinear elliptic boundary value problems in a convex polygonal (Formula presented.) Optimal and suboptimal order pointwise error estimates in the (Formula presented.) -seminorm and in the (Formula presented.) -norm are established on a shape-regular grid under the regularity assumptions (Formula presented.). Moreover, we propose some two-grid algorithms for the discontinuous Galerkin method which can be thought of as some type of linearization of the nonlinear system using a solution from a coarse finite element space. With this technique, solving a nonlinear elliptic problem on the fine finite element space is reduced into solving a linear problem on the fine finite element space and solving the nonlinear elliptic problem on a coarser space. Convergence estimates in a mesh-dependent energy norm are derived to justify the efficiency of the proposed two-grid algorithms. Numerical experiments are also provided to confirm our theoretical findings.
Original languageEnglish
Pages (from-to)153-175
Number of pages23
JournalJournal of Scientific Computing
Volume67
Issue number1
DOIs
Publication statusPublished - 1 Apr 2016

Keywords

  • Discontinuous Galerkin methods
  • Nonlinear problems
  • Pointwise error estimates
  • Two-grid algorithms

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Engineering(all)
  • Computational Theory and Mathematics

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