Monotone iterates for solving coupled systems of nonlinear parabolic equations
type: Item
instance of: scholarly article
title: Monotone iterates for solving coupled systems of nonlinear parabolic equations
zbMATH Open document ID: 1234.65033
published in: Computing
publication date: 2011-11-07T00:00:00Z
review text: When finite difference or finite element methods are applied to solve numerically systems of nonlinear parabolic partial differential equations, the corresponding discrete problem on each discrete time level is usually formulated as a system of nonlinear algebraic equations. A basic issue then is to guarantee that this system has a solution. Typically, some iterative method is used to construct numerical approximations to the resulting algebraic equations, so that the question of the convergence of the sequence of iterations is also relevant in this setting. In the paper under review, the technique of upper and lower solutions is considered as the iterative scheme. By using upper and lower solutions as initial iterations, two monotone sequences are constructed that converge monotonically from above and below to a solution of the problem. An analysis of convergence rates is also provided. In addition, a monotone domain decomposition for systems of nonlinear parabolic equations is achieved by combining the monotone approach with an iterative domain decomposition method. A numerical example derived from a gas-liquid interaction model is considered for illustrating the main theoretical results.
reviewed by: Fernando Casas
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 5968772
zbMATH Keywords: systems of nonlinear parabolic equations
zbMATH Keywords: system of nonlinear algebraic equations
zbMATH Keywords: iterative method
zbMATH Keywords: convergence
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: monotone domain decomposition
zbMATH Keywords: numerical example
author: Igor Boglaev
MaRDI profile type: Publication
full work available at URL: s00607-010-0132-x
OpenAlex ID: W1971709346
cites work: Numerical methods for coupled systems of nonlinear parabolic boundary value problems
cites work: Numerical Analysis of Coupled Systems of Nonlinear Parabolic Equations
cites work: Monotone algorithms for solving nonlinear monotone difference schemes of parabolic type in the canonical form
cites work: Domain decomposition for a parabolic convection-diffusion problem
cites work: Q4528992
DOI: 10.1007/S00607-010-0132-X
description: scientific article; zbMATH DE number 5968772