This is a major area of activity arising in many of the research topics. Of particular importance and interest is the development and analysis of algorithms for free boundary and interface problems, geometric PDEs and equations in complex domains. Progress requires a synthesis of mathematical modelling, analysis and computation, [A, C]. Partial differential equations on and for surfaces coupled to equations in complex bulk domains occur in many applications (fluid dynamics, materials science and cell biology) and usually the morphology of the surface is unknown, arbitrary, and changing in time. Examples include surface phase separation on biomembranes and electrical wave propagation in heart tissue. Numerical approaches include surface finite elements, phase field models, level sets and partition of unity methods. Within cell biology and material science it is of interest to extend methodologies to settings where discrete objects (e.g. macro-molecules) and continuous fields (e.g. concentrations) interact.
Researchers in this area: Barkley, Elliott, Kirkilionis, Stinner, Stuart