A stabilised finite element method for the convection-diffusion-reaction equation in mixed form

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Abstract

This paper is devoted to the approximation of the convection-diffusion-reaction equation using a mixed, first-order, formulation. We propose, and analyse, a stabilised finite element method that allows equal order interpolations for the primal and dual variables. This formulation, reminiscent of the Galerkin least-squares method, is proven stable and convergent. In addition, a numerical assessment of the numerical performance of different stabilised finite element methods for the mixed formulation is carried out, and the different methods are compared in terms of accuracy, stability, and sharpness of the layers for two different classical test problems.
Original languageEnglish
Pages (from-to)389-415
Number of pages37
JournalComputer Methods in Applied Mechanics and Engineering
Volume339
Early online date30 May 2018
DOIs
Publication statusPublished - 1 Sep 2018

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reaction-diffusion equations
finite element method
convection
Finite element method
formulations
Interpolation
sharpness
least squares method
interpolation
approximation
Convection

Keywords

  • convection-diffusion-reaction equation
  • Galerkin method
  • first-order formulation
  • stabilised finite element method
  • numerical comparisons

Cite this

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title = "A stabilised finite element method for the convection-diffusion-reaction equation in mixed form",
abstract = "This paper is devoted to the approximation of the convection-diffusion-reaction equation using a mixed, first-order, formulation. We propose, and analyse, a stabilised finite element method that allows equal order interpolations for the primal and dual variables. This formulation, reminiscent of the Galerkin least-squares method, is proven stable and convergent. In addition, a numerical assessment of the numerical performance of different stabilised finite element methods for the mixed formulation is carried out, and the different methods are compared in terms of accuracy, stability, and sharpness of the layers for two different classical test problems.",
keywords = "convection-diffusion-reaction equation, Galerkin method, first-order formulation, stabilised finite element method, numerical comparisons",
author = "Barrenechea, {Gabriel R.} and Poza, {Abner H.} and Heather Yorston",
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AU - Poza, Abner H.

AU - Yorston, Heather

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Y1 - 2018/9/1

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AB - This paper is devoted to the approximation of the convection-diffusion-reaction equation using a mixed, first-order, formulation. We propose, and analyse, a stabilised finite element method that allows equal order interpolations for the primal and dual variables. This formulation, reminiscent of the Galerkin least-squares method, is proven stable and convergent. In addition, a numerical assessment of the numerical performance of different stabilised finite element methods for the mixed formulation is carried out, and the different methods are compared in terms of accuracy, stability, and sharpness of the layers for two different classical test problems.

KW - convection-diffusion-reaction equation

KW - Galerkin method

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