Mixed mimetic spectral element method applied to Darcy’s problem

Pedro Pinto Rebelo; Artur Palha; Marc Gerritsma

doi:10.1007/978-3-319-01601-6

Mixed mimetic spectral element method applied to Darcy’s problem

Pedro Pinto Rebelo^*, Artur Palha, Marc Gerritsma

^*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

5 Citations (Scopus)

Abstract

We present a discretization for Darcy’s problem using the recently developed Mimetic Spectral Element Method (Kreeft et al. (2011) Mimetic framework on curvilinear quadrilaterals of arbitrary order. Submitted to FoCM, Arxiv preprint arXiv:1111.4304). The gist lies in the exact discrete representation of integral relations. In this paper, an anisotropic flow through a porous medium is considered and a discretization of a full permeability tensor is presented. The performance of the method is evaluated on standard test problems, converging at the same rate as the best possible approximation.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 - ICOSAHOM conference, Selected papers
Editors	Mejdi Azaïez, Jan S. Hesthaven, Henda El Fekih
Publisher	Springer
Pages	373-382
Number of pages	10
ISBN (Electronic)	9783319016009
DOIs	https://doi.org/10.1007/978-3-319-01601-6
Publication status	Published - 1 Jan 2014
Event	9th International Conference on Spectral and High Order Methods, ICOSAHOM 2012 - Gammarth, Tunisia Duration: 25 Jun 2012 → 29 Jun 2012

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	95
ISSN (Print)	1439-7358

Conference

Conference	9th International Conference on Spectral and High Order Methods, ICOSAHOM 2012
Country/Territory	Tunisia
City	Gammarth
Period	25/06/12 → 29/06/12

Access to Document

10.1007/978-3-319-01601-6

Cite this

Rebelo, P. P., Palha, A., & Gerritsma, M. (2014). Mixed mimetic spectral element method applied to Darcy’s problem. In M. Azaïez, J. S. Hesthaven, & H. E. Fekih (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 - ICOSAHOM conference, Selected papers (pp. 373-382). (Lecture Notes in Computational Science and Engineering; Vol. 95). Springer. https://doi.org/10.1007/978-3-319-01601-6

Rebelo, Pedro Pinto ; Palha, Artur ; Gerritsma, Marc. / Mixed mimetic spectral element method applied to Darcy’s problem. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 - ICOSAHOM conference, Selected papers. editor / Mejdi Azaïez ; Jan S. Hesthaven ; Henda El Fekih. Springer, 2014. pp. 373-382 (Lecture Notes in Computational Science and Engineering).

@inproceedings{158759dacc2d4fe4a1af3a2b4da6af74,

title = "Mixed mimetic spectral element method applied to Darcy{\textquoteright}s problem",

abstract = "We present a discretization for Darcy{\textquoteright}s problem using the recently developed Mimetic Spectral Element Method (Kreeft et al. (2011) Mimetic framework on curvilinear quadrilaterals of arbitrary order. Submitted to FoCM, Arxiv preprint arXiv:1111.4304). The gist lies in the exact discrete representation of integral relations. In this paper, an anisotropic flow through a porous medium is considered and a discretization of a full permeability tensor is presented. The performance of the method is evaluated on standard test problems, converging at the same rate as the best possible approximation.",

author = "Rebelo, {Pedro Pinto} and Artur Palha and Marc Gerritsma",

year = "2014",

month = jan,

day = "1",

doi = "10.1007/978-3-319-01601-6",

language = "English",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer",

pages = "373--382",

editor = "Mejdi Aza{\"i}ez and Hesthaven, {Jan S.} and Fekih, {Henda El}",

booktitle = "Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 - ICOSAHOM conference, Selected papers",

note = "9th International Conference on Spectral and High Order Methods, ICOSAHOM 2012 ; Conference date: 25-06-2012 Through 29-06-2012",

}

Rebelo, PP, Palha, A & Gerritsma, M 2014, Mixed mimetic spectral element method applied to Darcy’s problem. in M Azaïez, JS Hesthaven & HE Fekih (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 - ICOSAHOM conference, Selected papers. Lecture Notes in Computational Science and Engineering, vol. 95, Springer, pp. 373-382, 9th International Conference on Spectral and High Order Methods, ICOSAHOM 2012, Gammarth, Tunisia, 25/06/12. https://doi.org/10.1007/978-3-319-01601-6

Mixed mimetic spectral element method applied to Darcy’s problem. / Rebelo, Pedro Pinto; Palha, Artur ; Gerritsma, Marc.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 - ICOSAHOM conference, Selected papers. ed. / Mejdi Azaïez; Jan S. Hesthaven; Henda El Fekih. Springer, 2014. p. 373-382 (Lecture Notes in Computational Science and Engineering; Vol. 95).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - Mixed mimetic spectral element method applied to Darcy’s problem

AU - Rebelo, Pedro Pinto

AU - Palha, Artur

AU - Gerritsma, Marc

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We present a discretization for Darcy’s problem using the recently developed Mimetic Spectral Element Method (Kreeft et al. (2011) Mimetic framework on curvilinear quadrilaterals of arbitrary order. Submitted to FoCM, Arxiv preprint arXiv:1111.4304). The gist lies in the exact discrete representation of integral relations. In this paper, an anisotropic flow through a porous medium is considered and a discretization of a full permeability tensor is presented. The performance of the method is evaluated on standard test problems, converging at the same rate as the best possible approximation.

AB - We present a discretization for Darcy’s problem using the recently developed Mimetic Spectral Element Method (Kreeft et al. (2011) Mimetic framework on curvilinear quadrilaterals of arbitrary order. Submitted to FoCM, Arxiv preprint arXiv:1111.4304). The gist lies in the exact discrete representation of integral relations. In this paper, an anisotropic flow through a porous medium is considered and a discretization of a full permeability tensor is presented. The performance of the method is evaluated on standard test problems, converging at the same rate as the best possible approximation.

UR - http://www.scopus.com/inward/record.url?scp=84927616983&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-01601-6

DO - 10.1007/978-3-319-01601-6

M3 - Conference contribution

AN - SCOPUS:84927616983

T3 - Lecture Notes in Computational Science and Engineering

SP - 373

EP - 382

BT - Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 - ICOSAHOM conference, Selected papers

A2 - Azaïez, Mejdi

A2 - Hesthaven, Jan S.

A2 - Fekih, Henda El

PB - Springer

T2 - 9th International Conference on Spectral and High Order Methods, ICOSAHOM 2012

Y2 - 25 June 2012 through 29 June 2012

ER -

Rebelo PP, Palha A , Gerritsma M. Mixed mimetic spectral element method applied to Darcy’s problem. In Azaïez M, Hesthaven JS, Fekih HE, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 - ICOSAHOM conference, Selected papers. Springer. 2014. p. 373-382. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-01601-6

Mixed mimetic spectral element method applied to Darcy’s problem

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this