Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems

Bernardo Cockburn; Clint Dawson

doi:10.1023/A:1021203618109

Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems

Bernardo Cockburn, Clint Dawson

School of Mathematics

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

29 Scopus citations

Abstract

In this paper, we show how to couple the local discontinuous Galerkin method and the Raviart-Thomas mixed finite element method for elliptic equations modeling flow problems. We then show that the approximation of the velocity converges with the optimal order of k when we take the local discontinuous Galerkin that uses polynomials of degree k and the Raviart-Thomas space of polynomials of degree k-1.

Original language	English (US)
Pages (from-to)	505-522
Number of pages	18
Journal	Computational Geosciences
Volume	6
Issue number	3-4
DOIs	https://doi.org/10.1023/A:1021203618109
State	Published - 2002

Bibliographical note

Funding Information:
This work was funded in part by the National Science Foundation, project numbers DMS-9805491 and DMS-9873326. Bernardo Cockburn is partially supported by the National Science Foundation and the Minnesota Supercomputing Institute. Clint Dawson is partially supported by the National Science Foundation.

Keywords

Discontinuous Galerkin method
Elliptic equations
Mixed finite element method

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10.1023/A:1021203618109

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abstract = "In this paper, we show how to couple the local discontinuous Galerkin method and the Raviart-Thomas mixed finite element method for elliptic equations modeling flow problems. We then show that the approximation of the velocity converges with the optimal order of k when we take the local discontinuous Galerkin that uses polynomials of degree k and the Raviart-Thomas space of polynomials of degree k-1.",

keywords = "Discontinuous Galerkin method, Elliptic equations, Mixed finite element method",

author = "Bernardo Cockburn and Clint Dawson",

note = "Funding Information: This work was funded in part by the National Science Foundation, project numbers DMS-9805491 and DMS-9873326. Bernardo Cockburn is partially supported by the National Science Foundation and the Minnesota Supercomputing Institute. Clint Dawson is partially supported by the National Science Foundation.",

year = "2002",

doi = "10.1023/A:1021203618109",

language = "English (US)",

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journal = "Computational Geosciences",

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T1 - Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems

AU - Cockburn, Bernardo

AU - Dawson, Clint

N1 - Funding Information: This work was funded in part by the National Science Foundation, project numbers DMS-9805491 and DMS-9873326. Bernardo Cockburn is partially supported by the National Science Foundation and the Minnesota Supercomputing Institute. Clint Dawson is partially supported by the National Science Foundation.

PY - 2002

Y1 - 2002

N2 - In this paper, we show how to couple the local discontinuous Galerkin method and the Raviart-Thomas mixed finite element method for elliptic equations modeling flow problems. We then show that the approximation of the velocity converges with the optimal order of k when we take the local discontinuous Galerkin that uses polynomials of degree k and the Raviart-Thomas space of polynomials of degree k-1.

AB - In this paper, we show how to couple the local discontinuous Galerkin method and the Raviart-Thomas mixed finite element method for elliptic equations modeling flow problems. We then show that the approximation of the velocity converges with the optimal order of k when we take the local discontinuous Galerkin that uses polynomials of degree k and the Raviart-Thomas space of polynomials of degree k-1.

KW - Discontinuous Galerkin method

KW - Elliptic equations

KW - Mixed finite element method

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JO - Computational Geosciences

JF - Computational Geosciences

IS - 3-4

ER -

Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems

Abstract

Bibliographical note

Keywords

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