Discrete maximum principles for FE solutions of nonstationary diffusion-reaction problems with mixed boundary conditions

I. Faragó, Róbert Horváth, Sergey Korotov

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion-reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments.

Original languageEnglish
Pages (from-to)702-720
Number of pages19
JournalNumerical Methods for Partial Differential Equations
Volume27
Issue number3
DOIs
Publication statusPublished - May 2011

Fingerprint

Discrete Maximum Principle
Reaction-diffusion Problems
Maximum principle
Mixed Boundary Conditions
Discretization Method
Time Discretization
Theoretical Analysis
Numerical Experiment
Boundary conditions
Finite Element
Sufficient Conditions
Experiments

Keywords

  • angle condition
  • discrete maximum principle
  • linear finite elements
  • maximum principle; mixed boundary conditions
  • nonstationary diffusion-reaction problem
  • simplicial partition

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics
  • Analysis

Cite this

Discrete maximum principles for FE solutions of nonstationary diffusion-reaction problems with mixed boundary conditions. / Faragó, I.; Horváth, Róbert; Korotov, Sergey.

In: Numerical Methods for Partial Differential Equations, Vol. 27, No. 3, 05.2011, p. 702-720.

Research output: Contribution to journalArticle

@article{eae0b43659304e0190f2eef0eb6c702a,
title = "Discrete maximum principles for FE solutions of nonstationary diffusion-reaction problems with mixed boundary conditions",
abstract = "In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion-reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments.",
keywords = "angle condition, discrete maximum principle, linear finite elements, maximum principle; mixed boundary conditions, nonstationary diffusion-reaction problem, simplicial partition",
author = "I. Farag{\'o} and R{\'o}bert Horv{\'a}th and Sergey Korotov",
year = "2011",
month = "5",
doi = "10.1002/num.20547",
language = "English",
volume = "27",
pages = "702--720",
journal = "Numerical Methods for Partial Differential Equations",
issn = "0749-159X",
publisher = "John Wiley and Sons Inc.",
number = "3",

}

TY - JOUR

T1 - Discrete maximum principles for FE solutions of nonstationary diffusion-reaction problems with mixed boundary conditions

AU - Faragó, I.

AU - Horváth, Róbert

AU - Korotov, Sergey

PY - 2011/5

Y1 - 2011/5

N2 - In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion-reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments.

AB - In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion-reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments.

KW - angle condition

KW - discrete maximum principle

KW - linear finite elements

KW - maximum principle; mixed boundary conditions

KW - nonstationary diffusion-reaction problem

KW - simplicial partition

UR - http://www.scopus.com/inward/record.url?scp=79952968473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952968473&partnerID=8YFLogxK

U2 - 10.1002/num.20547

DO - 10.1002/num.20547

M3 - Article

VL - 27

SP - 702

EP - 720

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

SN - 0749-159X

IS - 3

ER -