Interfaces : modeling, analysis, numerics / Eberhard Bñsch, Klaus Deckelnick, Harald Garcke, Paola Pozzi.

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Interfaces : modeling, analysis, numerics / Eberhard Bñsch, Klaus Deckelnick, Harald Garcke, Paola Pozzi.

9783031355509 (electronic bk.)
3031355504 (electronic bk.)
9783031355493
3031355490

Cham, Switzerland : Birkhũser, 2023.

English

1 online resource (xii, 178 pages) : illustrations (some color).

10.1007/978-3-031-35550-9 doi

QA401 .B36 2023

511/.8

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.

Includes bibliographical references.

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Online resource; title from PDF title page (SpringerLink, viewed October 18, 2023).

Oberwolfach seminars ; 51.

Print version: 9783031355493

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