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Stokes–Darcy Equations

Analytic and Numerical Analysis

  • Book
  • © 2019

Overview

Authors:
  1. Ulrich Wilbrandt

    1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

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  • Thorough guide to the coupling of Stokes and Darcy equations
  • Includes numerical analysis and scientific computing
  • Almost all intermediate results are given with a rigorous proof
  • Special care is taken to analyze the difficult cases of non-smooth interfaces which are not completely enclosed in one subdomain

Part of the book series: Advances in Mathematical Fluid Mechanics (AMFM)

Part of the book sub series: Lecture Notes in Mathematical Fluid Mechanics (LNMFM)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Introduction

    • Ulrich Wilbrandt
    Pages 1-7

  3. Notation and Preliminary Results

    • Ulrich Wilbrandt
    Pages 9-25

  4. Properties of Sobolev Spaces

    • Ulrich Wilbrandt
    Pages 27-56

  5. Traces

    • Ulrich Wilbrandt
    Pages 57-82

  6. Subproblems Individually

    • Ulrich Wilbrandt
    Pages 83-108

  7. Stokes–Darcy Equations

    • Ulrich Wilbrandt
    Pages 109-151

  8. Algorithms

    • Ulrich Wilbrandt
    Pages 153-174

  9. Numerical Results

    • Ulrich Wilbrandt
    Pages 175-199

  10. Back Matter

    Pages 201-212
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Keywords

About this book

This book offers a thorough guide starting from fundamental functional analysis leading to the coupling of Stokes and Darcy equations, including numerical analysis and scientific computing. Almost all intermediate results are given with complete, rigorous proofs, including theorems which can be rarely found in the literature such that this book serves well as a reference on the topic. Special care is taken to analyze the difficult cases of non-smooth interfaces which are not completely enclosed in one subdomain, i.e, intersect with the outer boundary. This can hardly be found in the literature. Additionally, known and new subdomain iterative methods are introduced, analyzed and applied to standard examples as well as one example motivated by a geoscientific setting.



Reviews

“The entire book is clearly written, employs a modern notation, and with no doubt can be recommended to all researchers in this interesting field.” (Stanisław Migórski, zbMATH 1423.76005, 2019)


Authors and Affiliations

  • Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Ulrich Wilbrandt

Bibliographic Information

  • Book Title: Stokes–Darcy Equations

  • Book Subtitle: Analytic and Numerical Analysis

  • Authors: Ulrich Wilbrandt

  • Series Title: Advances in Mathematical Fluid Mechanics

  • DOI: https://doi.org/10.1007/978-3-030-02904-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Softcover ISBN: 978-3-030-02903-6Published: 11 January 2019

  • eBook ISBN: 978-3-030-02904-3Published: 10 January 2019

  • Series ISSN: 2297-0320

  • Series E-ISSN: 2297-0339

  • Edition Number: 1

  • Number of Pages: VIII, 212

  • Number of Illustrations: 20 b/w illustrations, 17 illustrations in colour

  • Topics: Functional Analysis, Numerical Analysis

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