Discontinuous Galerkin method for monotone nonlinear elliptic problems

Chunjia Bi, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)

Abstract

In this paper, we consider the incomplete interior penalty method for a class of second order monotone nonlinear elliptic problems. Using the theory of monotone operators, we show that the corresponding discrete method has a unique solution. The a priori error estimate in an energy norm is developed under the minimal regularity assumption on the exact solution, i.e., u Ie{cyrillic, ukrainian} H1 (Ω). Moreover, we propose a residual-based a posteriori error estimator and derive the computable upper and lower bounds on the error in an energy norm.
Original languageEnglish
Pages (from-to)991024
Number of pages1
JournalInternational Journal of Numerical Analysis and Modeling
Volume9
Issue number4
Publication statusPublished - 29 Jun 2012

Keywords

  • A posteriori error estimate
  • A priori error estimate
  • Discontinuous Galerkin method
  • Monotone
  • Nonlinear elliptic problems

ASJC Scopus subject areas

  • Numerical Analysis

Cite this