A stabilized mixed discontinuous Galerkin method for Darcy flow

Thomas J.R. Hughes; Arif Masud; Jing Wan

doi:10.1016/j.cma.2005.06.018

A stabilized mixed discontinuous Galerkin method for Darcy flow

Thomas J.R. Hughes, Arif Masud, Jing Wan

Research output: Contribution to journal › Article › peer-review

Abstract

A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes two- and three-dimensional constant-flow "patch tests" for distorted element geometries. The key ingredient in the formulation is a volumetric, residual-based, stabilization term that does not involve any mesh-dependent parameters.

Original language	English (US)
Pages (from-to)	3347-3381
Number of pages	35
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	195
Issue number	25-28
DOIs	https://doi.org/10.1016/j.cma.2005.06.018
State	Published - May 1 2006
Externally published	Yes

Keywords

Darcy flow
Discontinuous Galerkin method
Error estimates
Finite elements
Mass balance
Mixed method
Patch test
Stabilized method

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
Physics and Astronomy(all)
Computer Science Applications

Online availability

10.1016/j.cma.2005.06.018

Library availability

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title = "A stabilized mixed discontinuous Galerkin method for Darcy flow",

abstract = "A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes two- and three-dimensional constant-flow {"}patch tests{"} for distorted element geometries. The key ingredient in the formulation is a volumetric, residual-based, stabilization term that does not involve any mesh-dependent parameters.",

keywords = "Darcy flow, Discontinuous Galerkin method, Error estimates, Finite elements, Mass balance, Mixed method, Patch test, Stabilized method",

author = "Hughes, {Thomas J.R.} and Arif Masud and Jing Wan",

note = "Funding Information: The authors acknowledge the following sources of support: T.J.R. Hughes was supported by Office of Naval Research Grant No. N00014-03-1-0263 and by Sandia National Laboratories Contract No. A0340.0. A. Masud was supported by Office of Naval Research Grant No. N00014-02-1-0143. ",

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T1 - A stabilized mixed discontinuous Galerkin method for Darcy flow

AU - Hughes, Thomas J.R.

AU - Masud, Arif

AU - Wan, Jing

N1 - Funding Information: The authors acknowledge the following sources of support: T.J.R. Hughes was supported by Office of Naval Research Grant No. N00014-03-1-0263 and by Sandia National Laboratories Contract No. A0340.0. A. Masud was supported by Office of Naval Research Grant No. N00014-02-1-0143.

PY - 2006/5/1

Y1 - 2006/5/1

N2 - A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes two- and three-dimensional constant-flow "patch tests" for distorted element geometries. The key ingredient in the formulation is a volumetric, residual-based, stabilization term that does not involve any mesh-dependent parameters.

AB - A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes two- and three-dimensional constant-flow "patch tests" for distorted element geometries. The key ingredient in the formulation is a volumetric, residual-based, stabilization term that does not involve any mesh-dependent parameters.

KW - Darcy flow

KW - Discontinuous Galerkin method

KW - Error estimates

KW - Finite elements

KW - Mass balance

KW - Mixed method

KW - Patch test

KW - Stabilized method

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SP - 3347

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JO - Computer Methods in Applied Mechanics and Engineering

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ER -

A stabilized mixed discontinuous Galerkin method for Darcy flow

Abstract

Keywords

ASJC Scopus subject areas

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