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An Alternative Proof of a Strip Estimate for First-Order System Least-Squares for Interface Problems

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Large-Scale Scientific Computing (LSSC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10665))

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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 \(H ({\text {div}})\)-conforming Raviart-Thomas and standard \(H^1\)-conforming elements were used for the discretization. The interface condition is built directly in the \(H ({\text {div}})\)-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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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Duisburg-Essen, 45117, Essen, Germany

    Fleurianne Bertrand

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  1. Fleurianne Bertrand
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Correspondence to Fleurianne Bertrand .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Bertrand, F. (2018). An Alternative Proof of a Strip Estimate for First-Order System Least-Squares for Interface Problems. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_9

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  • DOI: https://doi.org/10.1007/978-3-319-73441-5_9

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  • Print ISBN: 978-3-319-73440-8

  • Online ISBN: 978-3-319-73441-5

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