E cient, accurate and exible Finite Element solvers for Chemotaxis problems

In the framework of Finite Element discretizations we introduce a fully nonlinear Newtonlike method and a linearized second order approach in time applied to certain partial differential equations for chemotactic processes incorporating two entities, a chemical agent and the reacting population of certain biological organisms/species. We investigate the bene t of a corresponding monolithic approach and the decoupled variant. In particular we analyze accuracy, e ciency and stability of the di erent methods and their dependencies on certain parameters in order to identify a well suited Finite Element solver for chemotaxis problems.