This monograph is centered on mathematical modeling, innovative numerical algorithms and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art phase-field fracture models are complemented with prototype explanations and rigorous numerical analysis. These developments are embedded into a carefully designed balance between scientific computing aspects and numerical modeling of nonstationary coupled variational inequality systems. Therein, a focus is on nonlinear solvers, goal-oriented error estimation, predictor-corrector adaptivity, and interface conditions. Engineering applications show the potential for tackling practical problems within the fields of solid mechanics, porous media, and fluidstructure interaction.

This monograph discusses modeling, adaptive discretisation techniques and the numerical solution of fluid structure interaction. An emphasis in part I lies on innovative discretisation and advanced interface resolution techniques. The second part covers the efficient and robust numerical solution of fluid-structure interaction. In part III, recent advances in the application fields vascular flows, binary-fluid-solid interaction, and coupling to fractures in the solid part are presented. Moreover each chapter provides a comprehensive overview in the respective topics including many references to concurring state-of-the art work. Contents Part I: Modeling and discretization On the implementation and benchmarking of an extended ALE method for FSI problems The locally adapted parametric finite element method for interface problems on triangular meshes An accurate Eulerian approach for fluid-structure interactions Part II: Solvers Numerical methods for unsteady thermal fluid structure interaction Recent development of robust monolithic fluid-structure interaction solvers A monolithic FSI solver applied to the FSI 1,2,3 benchmarks Part III: Applications Fluid-structure interaction for vascular flows: From supercomputers to laptops Binary-fluid-solid interaction based on the Navier-Stokes-Cahn-Hilliard Equations Coupling fluid-structure interaction with phase-field fracture: Algorithmic details

Dieses Lehrbuch behandelt zeitgemass, anwendungsorientiert und ausfuhrlich die theoretischen Grundlagen der Numerik. Dabei sind - zusatzlich zu den gangigen Inhalten - zahlreiche angewandte Beispiele und Praxis-Exkurse eingebunden, um das Verstandnis nachhaltig zu foerdern. Auf die sich wiederholenden, zentralen Kernkonzepte der Numerik (z.B. Stabilitat, Effizienz, Robustheit, Genauigkeit,...) wird explizit eingegangen, und diese Begriffe werden klar gegeneinander abgegrenzt. Ausserdem werden Numerische Verfahren der Linearen Algebra und der Analysis getrennt dargestellt, was den Studierenden den Zugang zur Numerik - ausgehend von den beiden Grundvorlesungen des Mathematik-Studiums - deutlich erleichtert.Das Buch ist daher sowohl fur Studierende der Mathematik als auch der Physik, der Informatik oder der Ingenieurwissenschaften bestens geeignet.

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