Advanced numerical treatment of chemotaxis driven PDEs in mathematical biology
| dc.contributor.advisor | Turek, Stefan | |
| dc.contributor.author | Strehl, Robert | |
| dc.contributor.referee | Blum, Heribert | |
| dc.date.accepted | 2013-07-18 | |
| dc.date.accessioned | 2013-08-06T05:29:47Z | |
| dc.date.available | 2013-08-06T05:29:47Z | |
| dc.date.issued | 2013-08-06 | |
| dc.description.abstract | From the first formulation of chemotaxis-driven partial differential equations (PDEs) by Keller and Segel in the 1970's up to the present, much effort has been expended in modelling complex chemotaxis re- lated processes. The shear complexity of such resulting PDEs crucially limits the postulation of analytical results. In this context the sup- port by numerical tools are of utmost interest and, thus, render the implementation of a numerically well elaborated solver an undoubt- edly important task. In this work I present different iteration strategies (linear/nonlinear, decoupled/monolithic) for chemotaxis-driven PDEs. The discretiza- tion follows the method of lines, where I employ finite elements to resolve the spatial discretization. I extensively study the numerical efficiency of the iteration strategies by applying them on particular chemotaxis models. Moreover, I demonstrate the need of numerical stabilization of chemotaxis-driven PDEs and apply a exible scalar algebraic ux correction. This methodology preserves the positivity of the fully discretized scheme under mild conditions and renders the numerical solution non-oscillatory at a low level of additional compu- tational costs. This work provides a first detailed study of accurate, efficient and exible finite element schemes for chemotaxis-driven PDEs and the implemented numerical framework provides a valuable basis for fu- ture applications of the solvers to more complex models. | |
| dc.identifier.uri | http://hdl.handle.net/2003/30452 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-10675 | |
| dc.language.iso | en | de |
| dc.subject | Algebraic flux correction | en |
| dc.subject | Blow up | en |
| dc.subject | Chemotaxis | en |
| dc.subject | Finite elements | en |
| dc.subject | Numerical efficiency | en |
| dc.subject | Stabilization | en |
| dc.subject.ddc | 510 | |
| dc.title | Advanced numerical treatment of chemotaxis driven PDEs in mathematical biology | en |
| dc.type | Text | de |
| dc.type.publicationtype | doctoralThesis | de |
| dcterms.accessRights | open access |