Compatible discretizations in our hearts and minds
by Marie E. Rognes (Simula Research Laboratory, Norway)
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.