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

Research output: Contribution to journalArticle

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.
LanguageEnglish
Number of pages35
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusAccepted/In press - 12 Apr 2018

Fingerprint

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

Cite this

@article{83b82d03eff148b99c780e5800621754,
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",
author = "Barrenechea, {Gabriel R.} and Poza, {Abner H.} and Heather Yorston",
year = "2018",
month = "4",
day = "12",
language = "English",
journal = "Computer Methods in Applied Mechanics end Engineering",
issn = "0045-7825",

}

TY - JOUR

T1 - A stabilised finite element method for the convection-diffusion-reaction equation in mixed form

AU - Barrenechea, Gabriel R.

AU - Poza, Abner H.

AU - Yorston, Heather

PY - 2018/4/12

Y1 - 2018/4/12

N2 - 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.

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

UR - https://www.sciencedirect.com/journal/computer-methods-in-applied-mechanics-and-engineering

M3 - Article

JO - Computer Methods in Applied Mechanics end Engineering

T2 - Computer Methods in Applied Mechanics end Engineering

JF - Computer Methods in Applied Mechanics end Engineering

SN - 0045-7825

ER -