Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems

Jinchao Xu, Aihui Zhou

Research output: Contribution to journalArticle

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In this paper, some local and parallel discretizations and adaptive finite element algorithms are proposed and analyzed for nonlinear elliptic boundary value problems in both two and three dimensions. The main technique is to use a standard finite element discretization on a coarse grid to approximate low frequencies and then to apply some linearized discretization on a fine grid to correct the resulted residual (which contains mostly high frequencies) by some local/parallel procedures. The theoretical tools for analyzing these methods are some local a priori and a posteriori error estimates for finite element solutions on general shape-regular grids that are also obtained in this paper.

Original languageEnglish (US)
Pages (from-to)293-327
Number of pages35
JournalAdvances in Computational Mathematics
Issue number4
Publication statusPublished - Jan 1 2001


All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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