The book aims to provide a comprehensive understanding of the most recent developments in finite volume methods. Its focus is on the development and analysis of these methods for the two- and three-dimensional Navier-Stokes equations, supported by extensive numerical results. It covers the most used lower-order finite element pairs, with well-posedness and optimal analysis for these finite volume methods.The authors have attempted to make this book self-contained by offering complete proofs and theoretical results. While most of the material presented has been taught by the authors in a number of institutions over the past several years, they also include several updated theoretical results for the finite volume methods for the incompressible Navier-Stokes equations. This book is primarily developed to address research needs for students and academic and industrial researchers. It is particularly valuable as a research reference in the fieldsof engineering, mathematics, physics, and computer sciences.

Autorentext

Dr. Jian Li is Professor at the Department of Mathematics, Shaanxi University of Science and Technology. He received special government allowances of the State Council and the honor of National Excellent Teacher. He published 76 papers in the famous international journals for the finite element methods/finite volume methods of the Navier-Stokes equations. Dr. Xiaolin Lin is Professor at the Department of Mathematics, Shaanxi University of Science and Technology. He received a Prominent Teacher of Shaanxi Province award and published 100 papers in the journals and 10 books in mathematics. Dr. Zhangxing Chen is Professor in the Department of Chemical and Petroleum Engineering and holds the NSERC/Energi Simulation Industrial Research Chair and Alberta Innovates Industrial Chair at the University of Calgary. His Ph.D. (1991), MSc (1985) and BS (1983) are from Purdue University, Xi'an Jiaotong University, and Nanchang (formerly, Jiangxi) University, respectively. He has authored and edited 23 books and published over 900 research articles. Dr. Chen is a Fellow of both Royal Society of Canada and Canadian Academy of Engineering and a Member of Chinese Academy of Engineering. His research interest is in Reservoir Engineering and Simulation and Renewable Energy.

Inhalt
Mathematical Foundation.- FVMs for the stationary Stokes equations.- FVMs for the stationary Navier-Stokes equations.- FVMs for the stationary for nonstationary Navier Stokes equations.- Glossary.