ENGLISH

Interfaces: Modeling, Analysis, Numerics

By Klaus Deckelnick , Harald Garcke , Eberhard Bänsch , Paola Pozzi

Book information

Publisher
Birkhäuser
Year
2023
ISBN
9783031355493, 9783031355509
DOI
10.1007/978-3-031-35550-9
Language
english
Format
PDF
Filesize
6 MB (6344184 bytes)
Series
Oberwolfach Seminars 51
Edition
1
Pages
178\186
Topic
Mathematics\\Geometry and Topology
Orientation
yes
Paginated
yes
Scanned
portrait
Time added
2023-10-12 15:59:23
Differential GeometryElastic FlowFinite Element MethodsFree Boundary ProblemsGeometric Evolution EquationsInterfacesLevel Set MethodMean Curvature FlowPhase Field MethodsTwo Phase Flow

Description

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.

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