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 Sep 2017 → 15 Sep 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).

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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",

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

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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

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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.

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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

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