Interfaces: Modeling, Analysis, Numerics / by Eberhard Bänsch, Klaus Deckelnick, Harald Garcke, Paola Pozzi.

Format:

Book

Author/Creator:

Bänsch, Eberhard.

Contributor:

Deckelnick, Klaus.

Garcke, Harald.

Pozzi, Paola.

Series:

Oberwolfach Seminars, 2296-5041 ; 51

Language:

English

Subjects (All):

Geometry, Differential.

Differential equations.

Differential Geometry.

Differential Equations.

Local Subjects:

Differential Geometry.

Differential Equations.

Physical Description:

1 online resource (186 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2023.

Summary:

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.

Contents:

1. Introduction

2. Some Notions from Differential Geometry

3. Modeling

4. Parametric Approaches for Geometric Evolution Equations and Interfaces

5. Implicit Approaches for Interfaces

6. Numerical Methods for Complex Interface Evolutions

7. Exercises.

ISBN:

3-031-35550-4