Robust preconditioning estimates for convection-dominated elliptic problems via a streamline Poincaré-Friedrichs inequality

Owe Axelsson, János Karátson, Balázs Kovács

Research output: Contribution to journalArticle

Abstract

This paper is devoted to the streamline diffusion finite element method, combined with equivalent preconditioning, for solving convection-dominated elliptic problems. The preconditioner is obtained from the streamline diffusion inner product. It is proved that the obtained convergence is robust, i.e., bounded independently of the perturbation parameter ε, for proper convection vector fields. The key to the estimates is an improved "streamline" Poincaré-Friedrichs inequality.

Original languageEnglish
Pages (from-to)2957-2976
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume52
Issue number6
DOIs
Publication statusPublished - Jan 1 2014

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Keywords

  • Poincaré-Friedrichs inequality
  • Robust preconditioning
  • Streamline diffusion finite element method

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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