02983nam 22005895 450 991075139360332120251009083516.03-031-35550-410.1007/978-3-031-35550-9(CKB)28487680100041(MiAaPQ)EBC30782894(Au-PeEL)EBL30782894(DE-He213)978-3-031-35550-9(PPN)272914606(MiAaPQ)EBC30781992(Au-PeEL)EBL30781992(EXLCZ)992848768010004120231010d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierInterfaces: Modeling, Analysis, Numerics /by Eberhard Bänsch, Klaus Deckelnick, Harald Garcke, Paola Pozzi1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Birkhäuser,2023.1 online resource (186 pages)Oberwolfach Seminars,2296-5041 ;519783031355493 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.Oberwolfach Seminars,2296-5041 ;51Geometry, DifferentialDifferential equationsDifferential GeometryDifferential EquationsGeometry, Differential.Differential equations.Differential Geometry.Differential Equations.516.36Bänsch Eberhard434179Deckelnick Klaus1432904Garcke Harald767190Pozzi Paola298291MiAaPQMiAaPQMiAaPQBOOK9910751393603321Interfaces: Modeling, Analysis, Numerics3577976UNINA