A review of reliable numerical models for three-dimensional linear parabolic problems

I. Faragó, R. Horváth

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The preservation of characteristic qualitative properties of different phenomena is a more and more important requirement in the construction of reliable numerical models. For phenomena that can be mathematically described by linear partial differential equations of parabolic type (such as the heat conduction, the diffusion, the pricing of options, etc.), the most important qualitative properties are: the maximum-minimum principle, the non-negativity preservation and the maximum norm contractivity. In this paper, we analyse the discrete analogues of the above properties for finite difference and finite element models, and we give a systematic overview of conditions that guarantee the required properties a priori. We have chosen the heat conduction process to illustrate the main concepts, but engineers and scientists involved in scientific computing can easily reformulate the results for other problems too.

Original languageEnglish
Pages (from-to)25-45
Number of pages21
JournalInternational Journal for Numerical Methods in Engineering
Volume70
Issue number1
DOIs
Publication statusPublished - Apr 2 2007

Fingerprint

Qualitative Properties
Parabolic Problems
Heat Conduction
Heat conduction
Preservation
Numerical models
Contractivity
Natural sciences computing
Minimum Principle
Three-dimensional
Maximum Norm
Scientific Computing
Nonnegativity
Linear partial differential equation
Finite Element Model
Partial differential equations
Pricing
Property A
Finite Difference
Analogue

Keywords

  • Discrete maximum principle
  • Heat conduction
  • Non-negativity preservation
  • Numerical solution
  • Qualitative properties

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Applied Mathematics
  • Computational Mechanics

Cite this

A review of reliable numerical models for three-dimensional linear parabolic problems. / Faragó, I.; Horváth, R.

In: International Journal for Numerical Methods in Engineering, Vol. 70, No. 1, 02.04.2007, p. 25-45.

Research output: Contribution to journalArticle

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