Compatible discretizations in our hearts and minds

The complexity and fragility of the human physiology matched against the cost and ethical concerns associated with experimental and clinical techniques sets a rich scene for mathematical modelling and simulation. In this talk, I'll focus on numerical and computational aspects of numerical methods for two emerging biomedical applications: (i) the brain's waterscape and (ii) finite collections of biological cells such as cardiac myocytes or pluripotent stem cells. Topics will include generalized poroelasticity, electrical signal propagation, diffusion-reaction problems over interfaces, mixed finite element discretizations, and preconditioning, and be illustrated by theoretical, numerical and computational results.