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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.
List of contents
Notation and preliminary results.- Properties of Sobolev spaces.- Traces.- Subproblems individually.- Stokes-Darcy equations.- Algorithms.- Numerical results.
Summary
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.
Additional text
“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)
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"The entire book is clearly written, employs a modern notation, and with no doubt can be recommended to all researchers in this interesting field." (Stanislaw Migórski, zbMATH 1423.76005, 2019)
