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Construction of Weight Functions of the Petrov–Galerkin Method for Convection–Diffusion–Reaction Equations in the Three-Dimensional Case

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Abstract

A method is proposed for constructing continuous piecewise-polynomial weight functions for the Petrov–Galerkin method in the three-dimensional domain. The form of such functions is determined by a finite number of variable parameters associated with edges of a grid partition. The choice of these parameters allows one to obtain numerical approximations for the original equation without non-physical oscillations with preserving an adequate accuracy. The results of the investigation are illustrated by several numerical examples.

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Authors and Affiliations

  1. NSAU-NASU Space Research Institute, Kyiv, Ukraine

    N. N. Salnikov

  2. National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine

    S. V. Siryk

Authors
  1. N. N. Salnikov
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  2. S. V. Siryk
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Correspondence to N. N. Salnikov.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 173–183, September–October, 2014.

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Salnikov, N.N., Siryk, S.V. Construction of Weight Functions of the Petrov–Galerkin Method for Convection–Diffusion–Reaction Equations in the Three-Dimensional Case. Cybern Syst Anal 50, 805–814 (2014). https://doi.org/10.1007/s10559-014-9671-z

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  • DOI: https://doi.org/10.1007/s10559-014-9671-z

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