A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation

G.R. Barrenechea, L.P. Franca, F. Valentin

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Starting from the non-stable p1/p0 discretization we build enhanced methods for the Darcy equation which are stable and locally mass-conservative. The methods are derived in a Petrov-Galerkin framework where both velocity and pressure trial spaces are enriched with multiscale functions. These functions solve local problems correcting the residuals of the strong equations in each element and interior edge, which leads to a velocity space enhanced with functions belonging to the lowest order Raviart-Thomas space. Several numerical tests validate the methods.
LanguageEnglish
Pages2449-2464
Number of pages15
JournalJournal of Sound and Vibration
Volume196
Issue number21-24
DOIs
Publication statusPublished - 2007

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Galerkin method
Galerkin methods
finite element method
Finite element method

Keywords

  • Darcy equation
  • finite element
  • Petrov-Galerkin method
  • enriching spaces
  • multiscales
  • applied mathematics
  • engineering

Cite this

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abstract = "Starting from the non-stable p1/p0 discretization we build enhanced methods for the Darcy equation which are stable and locally mass-conservative. The methods are derived in a Petrov-Galerkin framework where both velocity and pressure trial spaces are enriched with multiscale functions. These functions solve local problems correcting the residuals of the strong equations in each element and interior edge, which leads to a velocity space enhanced with functions belonging to the lowest order Raviart-Thomas space. Several numerical tests validate the methods.",
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A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation. / Barrenechea, G.R.; Franca, L.P.; Valentin, F.

In: Journal of Sound and Vibration, Vol. 196, No. 21-24, 2007, p. 2449-2464.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation

AU - Barrenechea, G.R.

AU - Franca, L.P.

AU - Valentin, F.

PY - 2007

Y1 - 2007

N2 - Starting from the non-stable p1/p0 discretization we build enhanced methods for the Darcy equation which are stable and locally mass-conservative. The methods are derived in a Petrov-Galerkin framework where both velocity and pressure trial spaces are enriched with multiscale functions. These functions solve local problems correcting the residuals of the strong equations in each element and interior edge, which leads to a velocity space enhanced with functions belonging to the lowest order Raviart-Thomas space. Several numerical tests validate the methods.

AB - Starting from the non-stable p1/p0 discretization we build enhanced methods for the Darcy equation which are stable and locally mass-conservative. The methods are derived in a Petrov-Galerkin framework where both velocity and pressure trial spaces are enriched with multiscale functions. These functions solve local problems correcting the residuals of the strong equations in each element and interior edge, which leads to a velocity space enhanced with functions belonging to the lowest order Raviart-Thomas space. Several numerical tests validate the methods.

KW - Darcy equation

KW - finite element

KW - Petrov-Galerkin method

KW - enriching spaces

KW - multiscales

KW - applied mathematics

KW - engineering

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U2 - 10.1016/j.cma.2007.01.004

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