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Interfacesmodeling, analysis, numerics /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Interfacesby Eberhard Bansch ... [et al.].
Reminder of title:	modeling, analysis, numerics /
other author:	Bansch, Eberhard.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	xii, 178 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Mathematical models.
Online resource:	https://doi.org/10.1007/978-3-031-35550-9
ISBN:	9783031355509$q(electronic bk.)

Interfacesmodeling, analysis, numerics /
Interfacesmodeling, analysis, numerics /[electronic resource] :by Eberhard Bansch ... [et al.]. - Cham :Springer Nature Switzerland :2023. - xii, 178 p. :ill. (some col.), digital ;24 cm. - Oberwolfach seminars,v. 512296-5041 ;. - Oberwolfach seminars ;44..

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.

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.

ISBN: 9783031355509$q(electronic bk.)

Standard No.: 10.1007/978-3-031-35550-9doiSubjects--Topical Terms:

182479
Mathematical models.

LC Class. No.: QA401

Dewey Class. No.: 511.8

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505 0 $a 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.
520 $a 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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