Advanced numerical treatment of chemotaxis-driven PDEs in mathematical biology. Focus on finite element discretization, iteration strategies and numerical efficiency (Q2863680)

This book is the doctoral thesis of the author.NEWLINENEWLINEChapter 1, the introduction, explains the biochemical concept of chemotaxis and gives the motivation for studying chemotaxis models.NEWLINENEWLINEChapter 2 presents preliminaries needed for understanding analytical results of some PDE models and their numerical treatment via finite element methods (FEM) used in this thesis.NEWLINENEWLINEChapter 3 summarizes the derivation of a classical model for chemotaxis and discusses some essential features of such a model.NEWLINENEWLINEChapter 4 describes different discretization schemes for a more general model of chemotaxis. In particular, it discusses a stabilization technique for remedying common drawbacks of standard discretization techniques.NEWLINENEWLINEChapter 5 focuses on some specific numerical techniques.NEWLINENEWLINEChapters 4 and 5 provide the numerical results obtained from the numerical analysis. Different discretization techniques are compared, their results are quantified and those that are most reliable, flexible and efficient for chemotaxis, are identified. These solvers are then applied to chemotaxis models recently discussed in the literature. Chapter 6 contains a summary and a discussion of fields for further investigation.