Format:
1 Online-Ressource
ISBN:
9783031355509
Series Statement:
Oberwolfach seminars volume 51
Content:
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.
Content:
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.
Additional Edition:
ISBN 9783031355493
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031355493
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031355516
Additional Edition:
Erscheint auch als Druck-Ausgabe Bänsch, Eberhard Interfaces Cham : Birkhäuser, 2023 ISBN 9783031355493
Language:
English
Subjects:
Mathematics
Keywords:
Grenzfläche
;
Mathematische Modellierung
;
Gradientenfluss
;
Parametrisierung
;
Evolutionsgleichung
;
Level-Set-Methode
;
Zweiphasenströmung
DOI:
10.1007/978-3-031-35550-9
Author information:
Garcke, Harald
Author information:
Pozzi, Paola
Author information:
Deckelnick, Klaus
