Interfaces: Modeling, Analysis, Numerics
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Beschreibung
These lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization.
We first give an introduction to classical methods from differential geometry and systematically derive the governing equations from physical principles. Then we will analyse parametric approaches to interface evolution problems and derive numerical methods which will be thoroughly analysed. In addition, implicit descriptions of interfaces such as phase field and level set methods will be analysed. Finally, we will discuss numerical methods for complex interface evolutions and will focus on two phase flow problems as an important example of such evolutions.
These lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization.
We first give an introduction to classical methods from differential geometry and systematically derive the governing equations from physical principles. Then we will analyse parametric approaches to interface evolution problems and derive numerical methods which will be thoroughly analysed. In addition, implicit descriptions of interfaces such as phase field and level set methods will be analysed. Finally, we will discuss numerical methods for complex interface evolutions and will focus on two phase flow problems as an important example of such evolutions.
Covers a vast array of different mathematical methods to deal with interfaces and free boundaries Includes in-depth numerical analysis of geometric partial differential equations and free boundary problems Provides a first systematic introduction to interfaces which combines modeling, analysis and computation
Autor*in
Eberhard Bänsch
Themen in »Interfaces: Modeling, Analysis, Numerics«
Interfaces Fluid Dynamics Mean Curvature Flow Elastic Flow Free Boundary Problems Phase Field Methods Level Set Method Parametric Approaches Differential Geometry Mathematical Modelling Finite Element Methods Partial Differential Equations Geometric Evolution Equations Two Phase Flow