PDE's on surfaces---a diffuse interface approach

By A. Ratz, Axel Voigt. 2006

153 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/d7e1974caa654ec9084fadc4052d2eeb4935addd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

1. Charles M. Elliott
2. Gerhard Dziuk
3. Harald Garcke
4. M. Roger
5. J. Kampmann
6. A. Ratz

In Computational Theory and Mathematics

1. Charles M. Elliott
2. Gerhard Dziuk
3. Harald Garcke
4. M. Roger
5. J. Kampmann
6. A. Ratz
7. Thomas R. Ranner
8. Arnold Reusken

In Materials Chemistry

1. Charles M. Elliott
2. Gerhard Dziuk
3. M. Roger
4. J. Kampmann
5. Harald Garcke
6. A. Ratz

Citations in the corpus

• Finite element methods for surface PDEs* (2013, methodology): “These arise in phase field approximations of interface problems (Caginalp 1989, Deckelnick et al. 2005), and it is natural to exploit the methodology to generate methods for solving partial differential equations on the interfaces (Rätz and Voigt 2006, Elliott, Stinner, Styles and Welford 2011).”
• A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes (2015, methodology): “Cahn–Hilliard systems on stationary surfaces have been numerically investigated by parametric finite elements [43], level set techniques [23] and with diffuse interface methods [43] mostly applied for the simulation of spinodal decomposition and coarsening scenarios.”