A stabilized mixed finite element method for Darcy flow based on a multiscale decomposition of the solution

K. B. Nakshatrala, D. Z. Turner, Keith Hjelmstad, A. Masud

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

Recently Masud and Hughes proposed a stabilized mixed finite element formulation for Darcy flow. An interesting feature of this formulation is that there are no mesh-dependent parameters. In the present work we provide a derivation of this formulation based on a multiscale decomposition of the solution. We also extend the work of Masud and Hughes to three-dimensional problems and show the convergence rates for various three-dimensional finite elements. We also show that this formulation passes three-dimensional constant-flow patch tests for distorted element geometries (i.e., elements with non-constant Jacobian). Robustness of this formulation is illustrated by performing numerical simulations on complex geometries.

Original languageEnglish (US)
Pages (from-to)4036-4049
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
Volume195
Issue number33-36
DOIs
StatePublished - Jul 1 2006
Externally publishedYes

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finite element method
Decomposition
decomposition
Finite element method
formulations
Geometry
patch tests
Computer simulation
geometry
mesh
derivation
simulation

Keywords

  • Darcy flow
  • Mixed methods
  • Multiscale formulation
  • Stabilized finite elements

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

Cite this

A stabilized mixed finite element method for Darcy flow based on a multiscale decomposition of the solution. / Nakshatrala, K. B.; Turner, D. Z.; Hjelmstad, Keith; Masud, A.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 33-36, 01.07.2006, p. 4036-4049.

Research output: Contribution to journalArticle

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