A discrete commutator theory for the consistency and phase error analysis of semi-discrete C0 finite element approximations to the linear transport equation

Travis Thompson

doi:10.1016/j.cam.2016.02.042

A discrete commutator theory for the consistency and phase error analysis of semi-discrete C0 finite element approximations to the linear transport equation

Travis Thompson

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

8 Scopus citations

Abstract

A novel method, based on a discrete commutator, for the analysis of consistency error and phase relations for semi-discrete continuous finite element approximation of the one-way wave equation is presented. The technique generalizes to arbitrary dimension, accommodates the use of compatible quadratures, does not require the use of complex calculations, is applicable on non-uniform mesh geometries, and is especially useful when conventional Taylor series or Fourier approaches are intractable. Following the theory the analysis method is demonstrated for several test cases.

Original language	English (US)
Pages (from-to)	229-248
Number of pages	20
Journal	Journal of Computational and Applied Mathematics
Volume	303
DOIs	https://doi.org/10.1016/j.cam.2016.02.042
State	Published - Sep 2016
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2021-04-02
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This work was supported by AFOSR grant FA99550-12-0358, National Science Foundation grants DMS-1217262 and DMS-1015984 and was partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST) (Texas A&M University, P.I. J.-L. Guermond) in addition to the partial support of National Science Foundation grant DMS-1312391 (Rice University, P.I. B. Rivière).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.cam.2016.02.042

Cite this

@article{d93d3107282d4c40bda67c5bdf3e61de,

title = "A discrete commutator theory for the consistency and phase error analysis of semi-discrete C0 finite element approximations to the linear transport equation",

abstract = "A novel method, based on a discrete commutator, for the analysis of consistency error and phase relations for semi-discrete continuous finite element approximation of the one-way wave equation is presented. The technique generalizes to arbitrary dimension, accommodates the use of compatible quadratures, does not require the use of complex calculations, is applicable on non-uniform mesh geometries, and is especially useful when conventional Taylor series or Fourier approaches are intractable. Following the theory the analysis method is demonstrated for several test cases.",

author = "Travis Thompson",

note = "KAUST Repository Item: Exported on 2021-04-02 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: This work was supported by AFOSR grant FA99550-12-0358, National Science Foundation grants DMS-1217262 and DMS-1015984 and was partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST) (Texas A&M University, P.I. J.-L. Guermond) in addition to the partial support of National Science Foundation grant DMS-1312391 (Rice University, P.I. B. Rivi{\`e}re). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2016",

month = sep,

doi = "10.1016/j.cam.2016.02.042",

language = "English (US)",

volume = "303",

pages = "229--248",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - A discrete commutator theory for the consistency and phase error analysis of semi-discrete C0 finite element approximations to the linear transport equation

AU - Thompson, Travis

N1 - KAUST Repository Item: Exported on 2021-04-02 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: This work was supported by AFOSR grant FA99550-12-0358, National Science Foundation grants DMS-1217262 and DMS-1015984 and was partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST) (Texas A&M University, P.I. J.-L. Guermond) in addition to the partial support of National Science Foundation grant DMS-1312391 (Rice University, P.I. B. Rivière). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2016/9

Y1 - 2016/9

N2 - A novel method, based on a discrete commutator, for the analysis of consistency error and phase relations for semi-discrete continuous finite element approximation of the one-way wave equation is presented. The technique generalizes to arbitrary dimension, accommodates the use of compatible quadratures, does not require the use of complex calculations, is applicable on non-uniform mesh geometries, and is especially useful when conventional Taylor series or Fourier approaches are intractable. Following the theory the analysis method is demonstrated for several test cases.

AB - A novel method, based on a discrete commutator, for the analysis of consistency error and phase relations for semi-discrete continuous finite element approximation of the one-way wave equation is presented. The technique generalizes to arbitrary dimension, accommodates the use of compatible quadratures, does not require the use of complex calculations, is applicable on non-uniform mesh geometries, and is especially useful when conventional Taylor series or Fourier approaches are intractable. Following the theory the analysis method is demonstrated for several test cases.

UR - http://hdl.handle.net/10754/668483

UR - https://linkinghub.elsevier.com/retrieve/pii/S037704271630098X

UR - http://www.scopus.com/inward/record.url?scp=84962331737&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2016.02.042

DO - 10.1016/j.cam.2016.02.042

M3 - Article

SN - 0377-0427

VL - 303

SP - 229

EP - 248

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

A discrete commutator theory for the consistency and phase error analysis of semi-discrete C0 finite element approximations to the linear transport equation

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this