Stokes–Darcy Equations: Analytic and Numerical Analysis

Description

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. Front Matter ....Pages i-viii Introduction (Ulrich Wilbrandt)....Pages 1-7 Notation and Preliminary Results (Ulrich Wilbrandt)....Pages 9-25 Properties of Sobolev Spaces (Ulrich Wilbrandt)....Pages 27-56 Traces (Ulrich Wilbrandt)....Pages 57-82 Subproblems Individually (Ulrich Wilbrandt)....Pages 83-108 Stokes–Darcy Equations (Ulrich Wilbrandt)....Pages 109-151 Algorithms (Ulrich Wilbrandt)....Pages 153-174 Numerical Results (Ulrich Wilbrandt)....Pages 175-199 Back Matter ....Pages 201-212