An alternative proof of a strip estimate for first-order system least-squares for interface problems

Fleurianne Bertrand

doi:10.1007/978-3-319-73441-5_9

An alternative proof of a strip estimate for first-order system least-squares for interface problems

Fleurianne Bertrand^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

The purpose of this paper is an alternative proof of a strip estimate, used in Least-Squares methods for interface problems, as in [4] for a two-phase flow problem with incompressible flow in the subdomains. The Stokes flow problems in the subdomains are treated as first-order systems and a combination of H(div) -conforming Raviart-Thomas and standard H¹ -conforming elements were used for the discretization. The interface condition is built directly in the H(div) -conforming space. Using the strip estimate, the homogeneous Least-Squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates.

Original language	English
Title of host publication	Large-Scale Scientific Computing
Subtitle of host publication	11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017, Revised Selected Papers
Editors	Ivan Lirkov, Svetozar Margenov
Place of Publication	Cham
Publisher	Springer
Pages	95-102
Number of pages	8
ISBN (Electronic)	978-3-319-73441-5
ISBN (Print)	978-3-319-73440-8
DOIs	https://doi.org/10.1007/978-3-319-73441-5_9
Publication status	Published - 2018
Externally published	Yes
Event	11th International Conference on Large-Scale Scientific Computations, LSSC 2017 - Sozopol, Bulgaria Duration: 11 Sept 2017 → 15 Sept 2017 Conference number: 11

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	10665
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Conference on Large-Scale Scientific Computations, LSSC 2017
Abbreviated title	LSSC 2017
Country/Territory	Bulgaria
City	Sozopol
Period	11/09/17 → 15/09/17

Access to Document

10.1007/978-3-319-73441-5_9

Cite this

Bertrand, F. (2018). An alternative proof of a strip estimate for first-order system least-squares for interface problems. In I. Lirkov, & S. Margenov (Eds.), Large-Scale Scientific Computing: 11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017, Revised Selected Papers (pp. 95-102). (Lecture Notes in Computer Science; Vol. 10665). Springer. https://doi.org/10.1007/978-3-319-73441-5_9

Bertrand, Fleurianne. / An alternative proof of a strip estimate for first-order system least-squares for interface problems. Large-Scale Scientific Computing: 11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017, Revised Selected Papers. editor / Ivan Lirkov ; Svetozar Margenov. Cham : Springer, 2018. pp. 95-102 (Lecture Notes in Computer Science).

@inproceedings{15f0bb79ed944d949f922602d0e810a8,

title = "An alternative proof of a strip estimate for first-order system least-squares for interface problems",

abstract = "The purpose of this paper is an alternative proof of a strip estimate, used in Least-Squares methods for interface problems, as in [4] for a two-phase flow problem with incompressible flow in the subdomains. The Stokes flow problems in the subdomains are treated as first-order systems and a combination of H(div) -conforming Raviart-Thomas and standard H1 -conforming elements were used for the discretization. The interface condition is built directly in the H(div) -conforming space. Using the strip estimate, the homogeneous Least-Squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates.",

author = "Fleurianne Bertrand",

year = "2018",

doi = "10.1007/978-3-319-73441-5\_9",

language = "English",

isbn = "978-3-319-73440-8",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "95--102",

editor = "Ivan Lirkov and Svetozar Margenov",

booktitle = "Large-Scale Scientific Computing",

address = "Germany",

note = "11th International Conference on Large-Scale Scientific Computations, LSSC 2017, LSSC 2017 ; Conference date: 11-09-2017 Through 15-09-2017",

}

Bertrand, F 2018, An alternative proof of a strip estimate for first-order system least-squares for interface problems. in I Lirkov & S Margenov (eds), Large-Scale Scientific Computing: 11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017, Revised Selected Papers. Lecture Notes in Computer Science, vol. 10665, Springer, Cham, pp. 95-102, 11th International Conference on Large-Scale Scientific Computations, LSSC 2017, Sozopol, Bulgaria, 11/09/17. https://doi.org/10.1007/978-3-319-73441-5_9

An alternative proof of a strip estimate for first-order system least-squares for interface problems. / Bertrand, Fleurianne.
Large-Scale Scientific Computing: 11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017, Revised Selected Papers. ed. / Ivan Lirkov; Svetozar Margenov. Cham: Springer, 2018. p. 95-102 (Lecture Notes in Computer Science; Vol. 10665).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - An alternative proof of a strip estimate for first-order system least-squares for interface problems

AU - Bertrand, Fleurianne

N1 - Conference code: 11

PY - 2018

Y1 - 2018

N2 - The purpose of this paper is an alternative proof of a strip estimate, used in Least-Squares methods for interface problems, as in [4] for a two-phase flow problem with incompressible flow in the subdomains. The Stokes flow problems in the subdomains are treated as first-order systems and a combination of H(div) -conforming Raviart-Thomas and standard H1 -conforming elements were used for the discretization. The interface condition is built directly in the H(div) -conforming space. Using the strip estimate, the homogeneous Least-Squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates.

AB - The purpose of this paper is an alternative proof of a strip estimate, used in Least-Squares methods for interface problems, as in [4] for a two-phase flow problem with incompressible flow in the subdomains. The Stokes flow problems in the subdomains are treated as first-order systems and a combination of H(div) -conforming Raviart-Thomas and standard H1 -conforming elements were used for the discretization. The interface condition is built directly in the H(div) -conforming space. Using the strip estimate, the homogeneous Least-Squares functional is shown to be equivalent to an appropriate norm allowing the use of standard finite element approximation estimates.

UR - https://www.scopus.com/pages/publications/85041716723

U2 - 10.1007/978-3-319-73441-5_9

DO - 10.1007/978-3-319-73441-5_9

M3 - Conference contribution

AN - SCOPUS:85041716723

SN - 978-3-319-73440-8

T3 - Lecture Notes in Computer Science

SP - 95

EP - 102

BT - Large-Scale Scientific Computing

A2 - Lirkov, Ivan

A2 - Margenov, Svetozar

PB - Springer

CY - Cham

T2 - 11th International Conference on Large-Scale Scientific Computations, LSSC 2017

Y2 - 11 September 2017 through 15 September 2017

ER -

Bertrand F. An alternative proof of a strip estimate for first-order system least-squares for interface problems. In Lirkov I, Margenov S, editors, Large-Scale Scientific Computing: 11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017, Revised Selected Papers. Cham: Springer. 2018. p. 95-102. (Lecture Notes in Computer Science). doi: 10.1007/978-3-319-73441-5_9

An alternative proof of a strip estimate for first-order system least-squares for interface problems

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this