Mathematical modelling with PDEs is nowadays an integral part of research and development in many areas of the life sciences and complements or even replaces experimental studies. Such models require dedicated numerical tools for their simulation but also for their optimal control and the understanding of the impact of uncertainties. Currently also data-driven tools and their combination with traditional numerical schemes are increasingly investigated.
We develop, analyse, implement and test dedicated numerical methods for PDE models from biology and medicine with a focus on accuracy, efficiency but also on qualitative properties like conservation of mass and the non-negativity of solutions. The range of models under investigation is broad and includes models of calcium waves on the heart, normal and abnormal cell migration in tissues, pattern formation, cellular and matrix-related changes for osteoarthritis, and the spreading of infections.
