Mass-conservative coupling of bulk and surface processes on implicit, time-dependent domains

• Applicant: Professor Dr. Christian Engwer
• Subject Area: Mathematics
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 257639540

The aim of this project proposal is the development of a numerical method for solving partial differential equations (PDEs) on evolving, i.e. time-dependent, surfaces which are coupled to PDEs on the enclosed bulk. Coupled bulk-surface problems arise in many applications; for example in fluid dynamics and biological applications.The project yields contributions to the development of numerical methods, the analysis of these methods, their efficient implementation and their validation.In the course of this, the central challenge is to develop a scheme for surface PDEs which is locally mass-conservative and at the same time allows for strong deformations that might exhibit an anisotropic nature and even topology changes. We will use an implicit description of the surface which allows for a simple handling of geometry changes. This representation is also very well suited to incorporate image data, like CT or microscopy data.

• DFG Programme: Research Grants