Efficient, accurate and flexible finite element solvers for chemotaxis problems

In the framework of finite element discretizations, we introduce a fully nonlinear Newton-like 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 benefit of a corresponding monolithic approach and the decoupled variant. In particular, we analyze accuracy, efficiency and stability of different methods and their dependences on certain parameters in order to identify a well suited finite element solver for chemotaxis problems.