FOSLL∗ for nonlinear partial differential equations

Eunjung Lee, Thomas A. Manteuffel, Chad R. Westphal

Research output: Contribution to journalArticle

Abstract

In previous work, the first-order system LL∗ (FOSLL∗) method was developed for linear partial differential equations. This approach seeks to minimize the residual of the equations in a dual norm induced by the differential operator, yielding approximations accurate in L2(Ω) rather than H1(Ω) or H(Div). In this paper, the general framework of FOSLL∗ is extended to a wide range of nonlinear problems. Four approaches to propagating an inexact Newton iteration based on a FOSLL∗ approximation are presented, and theory for robust convergence in L2(Ω) is established. Numerical results are presented for two formulations of the steady incompressible Navier-Stokes equations and for a diffusion equation with reduced regularity due to a discontinuous diffusion coefficient.

Original languageEnglish
Pages (from-to)S503-S525
JournalSIAM Journal on Scientific Computing
Volume37
Issue number5
DOIs
Publication statusPublished - 2015 Jan 1

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All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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