Bücher der Reihe Necas Center Series

This book provides essential lecture notes on solving large linear saddle-point systems, which arise in a wide range of applications and often pose computational challenges in science and engineering.

This book addresses the basic concepts of continuum mechanics, that is, the classical field theory of deformable bodies. The theory is systematically developed, from the kinematics to the balance equations, the material theory, and the entropy principles.

The book presents recent results and new trends in the theory of fluid mechanics. Each of the four chapters focuses on a different problem in fluid flow accompanied by an overview of available older results.The chapters are extended lecture notes from the ESSAM school "Mathematical Aspects of Fluid Flows" held in Kácov (Czech Republic) in May/June 2017.The lectures were presented by Dominic Breit (Heriot-Watt University Edinburgh), Yann Brenier (École Polytechnique, Palaiseau), Pierre-Emmanuel Jabin (University of Maryland) and Christian Rohde (Universität Stuttgart), and cover various aspects of mathematical fluid mechanics - from Euler equations, compressible Navier-Stokes equations and stochastic equations in fluid mechanics to equations describing two-phase flow; from the modeling and mathematical analysis of equations to numerical methods. Although the chapters feature relatively recent results, they are presented in a form accessible to PhD students in the field of mathematical fluid mechanics.

Since expertise in various fields is necessary, this calls for a multidisciplinary approach. This edited volume connects basic physical, biological, and physiological concepts to methods for the mathematical modeling of various materials by pursuing a multiscale approach, from subcellular to organ and system level.

This book introduces a class of alignment models based on the so-called Cucker-Smale system as well as its kinetic and hydrodynamic counterparts.

Introduction.- Metric Based Mesh Representation.- Interpolation Error Estimates for Two Dimensions.- Interpolation Error Estimates for Three Dimensions.- Anisotropic Mesh Adaptation, h-Variant.- Anisotropic Mesh Adaptation Method, hp-Variant.- Framework of the Goal-Oriented Error Estimates.- Goal-Oriented Anisotropic Mesh Adaptation.- Implementation Aspects.- Applications.