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Discrete Energy Laws for the First-Order System Least-Squares Finite-Element Approach Read chapter Read first chapter

2018 | OriginalPaper | Chapter

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

Author : Fleurianne Bertrand

Published in: Large-Scale Scientific Computing

Publisher: Springer International Publishing

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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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previous chapter Two Classes of Vector Domain Decomposition Schemes for Time-Dependent Problems with Overlapping Subdomains
next chapter Spectral Mimetic Least-Squares Method for Div-curl Systems
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Metadata
Title
An Alternative Proof of a Strip Estimate for First-Order System Least-Squares for Interface Problems
Author
Fleurianne Bertrand
Copyright Year
2018
Book
Large-Scale Scientific Computing

Print ISBN: 978-3-319-73440-8

Electronic ISBN: 978-3-319-73441-5

Copyright Year: 2018

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

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