Newton- LL method for the second-order semi-linear elliptic partial differential equations

Research output: Contribution to journalArticle

Abstract

Newton's method with first-order system least squares (FOSLS) finite element method has been widely used to approximately solve a system of nonlinear partial differential equations (Adler et al., 2010 [9], Codd et al., 2003 [10], Manteuffel et al., 2006 [11]). In this paper, we propose to use the first order system LL method to find a correction in each Newton's iteration which provides an L2-approximation of the second-order semi-linear elliptic partial differential equations while the typical Newton-FOSLS method providesH1-approximations. The numerical tests have been conducted to validate the theory.

Original languageEnglish
Pages (from-to)1031-1044
Number of pages14
JournalComputers and Mathematics with Applications
Volume69
Issue number10
DOIs
Publication statusPublished - 2015 May 1

All Science Journal Classification (ASJC) codes

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

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