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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First-order System
Nonlinear Partial Differential Equations
Partial differential equations
Navier Stokes equations
Discontinuous Coefficients
Newton Iteration
Linear partial differential equation
Incompressible Navier-Stokes Equations
Approximation
Diffusion equation
Diffusion Coefficient
Nonlinear Problem
Differential operator
Regularity
Minimise
Norm
Numerical Results
Formulation
Range of data

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Computational Mathematics

Cite this

Lee, Eunjung ; Manteuffel, Thomas A. ; Westphal, Chad R. / FOSLL∗ for nonlinear partial differential equations. In: SIAM Journal on Scientific Computing. 2015 ; Vol. 37, No. 5. pp. S503-S525.
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FOSLL∗ for nonlinear partial differential equations. / Lee, Eunjung; Manteuffel, Thomas A.; Westphal, Chad R.

In: SIAM Journal on Scientific Computing, Vol. 37, No. 5, 01.01.2015, p. S503-S525.

Research output: Contribution to journalArticle

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